evaluate.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from generate_access_graph import generate_iam_test\n",
    "import time\n",
    "from z3 import Solver, sat, StringVal, BoolVal, unsat\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import average\n",
    "\n",
    "\n",
    "def time_function(f, *args):\n",
    "    start = time.perf_counter()\n",
    "    result = f(*args)\n",
    "    end = time.perf_counter()\n",
    "    return (result, end-start)\n",
    "\n",
    "def perform_test(params, id):\n",
    "    test_instance = generate_iam_test(params)\n",
    "    (user, action, res, path_len) = test_instance.generate_allow_test()\n",
    "    print(user)\n",
    "    print(action)\n",
    "    print(res)\n",
    "    s = Solver()\n",
    "    s.add(test_instance.env['Allow'](StringVal(user), StringVal(action), StringVal(res)))\n",
    "    (result, elapsed) = time_function(lambda: s.check())\n",
    "    #print(f\"test-{id}: params={params}; path_length={path_len}; num_roles={len(test_instance.role_graph)} q=Allow({user}, {action}, {res}); elapsed={elapsed}\")\n",
    "    if result == sat:\n",
    "        print('sat')\n",
    "    else:\n",
    "        print('unsat')\n",
    "    \n",
    "    return {'result': result == 'sat', 'params': params, 'path_length': path_len, 'num_roles': len(test_instance.role_graph), 'q': f\"Allow({user}, {action}, {res})\", \n",
    "                                    'elapsed': elapsed}\n",
    "\n",
    "def perform_averaged_test(params, iters=10):\n",
    "    test_instance = generate_iam_test(params)\n",
    "\n",
    "    times = []\n",
    "    results = []\n",
    "    for _ in range(iters):\n",
    "        (user, action, res) = test_instance.generate_random_allow_test()\n",
    "        s = Solver()\n",
    "        s.add(test_instance.env['Allow'](StringVal(user), StringVal(action), StringVal(res)))\n",
    "        #print(f\"query: {test_instance.env['Allow'](StringVal(user), StringVal(action), StringVal(res))}\")\n",
    "        (result, elapsed) = time_function(lambda: s.check())\n",
    "        if result == unsat:\n",
    "            print('unsat!')\n",
    "            s1 = Solver()\n",
    "            s1.add(test_instance.env['TC_Access'](StringVal(user), StringVal(role)))\n",
    "            print(f\"checking access: {s1.check()}\")\n",
    "\n",
    "            s2 = Solver()\n",
    "            s2.add(test_instance.env['Policy'](BoolVal(True), StringVal(role), StringVal(action),\\\n",
    "                            StringVal(res)))\n",
    "            print(f\"checking policy: {s1.check()}\")\n",
    "            assert result == sat\n",
    "\n",
    "\n",
    "        times.append(elapsed)\n",
    "        results.append(result)\n",
    "    \n",
    "    return {'result': results, 'params': params,  'num_roles': len(test_instance.role_graph), \n",
    "                                    'avg_elapsed': average(times)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arn:aws:iam::14354624986284130233:user/user_95\n",
      "s3:GetObjectRetention\n",
      "test_object_541\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 2, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 235, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_95, s3:GetObjectRetention, test_object_541)', 'elapsed': 0.3605761930011795}\n",
      "arn:aws:iam::14354624986284130233:user/user_84\n",
      "s3:PutObject\n",
      "test_object_1086\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 4, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 238, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_84, s3:PutObject, test_object_1086)', 'elapsed': 0.5002497749992472}\n",
      "arn:aws:iam::14354624986284130233:user/user_42\n",
      "s3:DeleteObjectVersion\n",
      "test_object_1778\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 6, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 249, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_42, s3:DeleteObjectVersion, test_object_1778)', 'elapsed': 0.4899934899985965}\n",
      "arn:aws:iam::14354624986284130233:user/user_35\n",
      "s3:GetObject\n",
      "test_object_2503\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 8, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 12, 'num_roles': 269, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_35, s3:GetObject, test_object_2503)', 'elapsed': 0.5782670810003765}\n",
      "arn:aws:iam::14354624986284130233:user/user_29\n",
      "s3:GetObjectRetention\n",
      "test_object_3096\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 10, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 11, 'num_roles': 242, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_29, s3:GetObjectRetention, test_object_3096)', 'elapsed': 0.5232485749984335}\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[4], line 16\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[39mfor\u001b[39;00m n \u001b[39min\u001b[39;00m branching_factors:\n\u001b[1;32m     15\u001b[0m     params1[\u001b[39m'\u001b[39m\u001b[39mrole_branching_factor\u001b[39m\u001b[39m'\u001b[39m] \u001b[39m=\u001b[39m n\n\u001b[0;32m---> 16\u001b[0m     r \u001b[39m=\u001b[39m perform_test(params1, n)\n\u001b[1;32m     17\u001b[0m     \u001b[39mprint\u001b[39m(r)\n\u001b[1;32m     18\u001b[0m     \u001b[39mif\u001b[39;00m r[\u001b[39m'\u001b[39m\u001b[39mpath_length\u001b[39m\u001b[39m'\u001b[39m] \u001b[39mnot\u001b[39;00m \u001b[39min\u001b[39;00m path_lengths:\n",
      "Cell \u001b[0;32mIn[3], line 11\u001b[0m, in \u001b[0;36mperform_test\u001b[0;34m(params, id)\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mperform_test\u001b[39m(params, \u001b[39mid\u001b[39m):\n\u001b[0;32m---> 11\u001b[0m     test_instance \u001b[39m=\u001b[39m generate_iam_test(params)\n\u001b[1;32m     12\u001b[0m     (user, action, res, path_len) \u001b[39m=\u001b[39m test_instance\u001b[39m.\u001b[39mgenerate_allow_test()\n\u001b[1;32m     13\u001b[0m     \u001b[39mprint\u001b[39m(user)\n",
      "File \u001b[0;32m~/Dev/csc564Project/generate_access_graph.py:231\u001b[0m, in \u001b[0;36mgenerate_iam_test\u001b[0;34m(params)\u001b[0m\n\u001b[1;32m    228\u001b[0m all_policies \u001b[39m=\u001b[39m \u001b[39mlist\u001b[39m(\u001b[39mzip\u001b[39m(policy_arns, policy_dicts)) \u001b[39m+\u001b[39m \u001b[39mlist\u001b[39m(\u001b[39mzip\u001b[39m(role_arns, role_dicts))\n\u001b[1;32m    230\u001b[0m \u001b[39m#print(all_policies)\u001b[39;00m\n\u001b[0;32m--> 231\u001b[0m env \u001b[39m=\u001b[39m transpile(all_policies)\n\u001b[1;32m    233\u001b[0m \u001b[39mreturn\u001b[39;00m IAMTestConfiguration(params, env, role_to_user, role_to_pairs, nx\u001b[39m.\u001b[39mDiGraph(adj))\n",
      "File \u001b[0;32m~/Dev/csc564Project/policy.py:199\u001b[0m, in \u001b[0;36mtranspile\u001b[0;34m(policies)\u001b[0m\n\u001b[1;32m    198\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mtranspile\u001b[39m(policies):\n\u001b[0;32m--> 199\u001b[0m     policy \u001b[39m=\u001b[39m createPolicyFunction(policies)\n\u001b[1;32m    201\u001b[0m     access \u001b[39m=\u001b[39m RecFunction(\u001b[39m'\u001b[39m\u001b[39mAccess\u001b[39m\u001b[39m'\u001b[39m, StringSort(), StringSort(), BoolSort())\n\u001b[1;32m    202\u001b[0m     u1, u2 \u001b[39m=\u001b[39m Strings(\u001b[39m'\u001b[39m\u001b[39mu1 u2\u001b[39m\u001b[39m'\u001b[39m)\n",
      "File \u001b[0;32m~/Dev/csc564Project/policy.py:119\u001b[0m, in \u001b[0;36mcreatePolicyFunction\u001b[0;34m(ls)\u001b[0m\n\u001b[1;32m    116\u001b[0m r \u001b[39m=\u001b[39m String(\u001b[39m'\u001b[39m\u001b[39mr\u001b[39m\u001b[39m'\u001b[39m)\n\u001b[1;32m    118\u001b[0m Policy \u001b[39m=\u001b[39m RecFunction(\u001b[39m'\u001b[39m\u001b[39mPolicy\u001b[39m\u001b[39m'\u001b[39m, BoolSort(), StringSort(), StringSort(), StringSort(), BoolSort())\n\u001b[0;32m--> 119\u001b[0m RecAddDefinition(Policy, [e, u, a, r], usePolicyConstraints(e, u, a, r, \n\u001b[1;32m    120\u001b[0m                     \u001b[39mlist\u001b[39;49m(\u001b[39mmap\u001b[39;49m(\u001b[39mlambda\u001b[39;49;00m user_policy: generatePolicyConstraints(\u001b[39m*\u001b[39;49muser_policy),ls))))\n\u001b[1;32m    122\u001b[0m \u001b[39mreturn\u001b[39;00m Policy\n",
      "File \u001b[0;32m~/Dev/csc564Project/policy.py:107\u001b[0m, in \u001b[0;36musePolicyConstraints\u001b[0;34m(e, u, a, r, ls)\u001b[0m\n\u001b[1;32m    104\u001b[0m     x1,x2,x3,x4 \u001b[39m=\u001b[39m l\n\u001b[1;32m    105\u001b[0m     \u001b[39mreturn\u001b[39;00m And(x1(e),x2(u),Or(\u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(\u001b[39mlambda\u001b[39;00m x : x(a),x3))),Or(\u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(\u001b[39mlambda\u001b[39;00m x : x(r),x4))))\n\u001b[0;32m--> 107\u001b[0m \u001b[39mreturn\u001b[39;00m Or(\u001b[39mlist\u001b[39;49m(\u001b[39mmap\u001b[39;49m(openParams,ls)))\n",
      "File \u001b[0;32m~/Dev/csc564Project/policy.py:105\u001b[0m, in \u001b[0;36musePolicyConstraints.<locals>.openParams\u001b[0;34m(l)\u001b[0m\n\u001b[1;32m    103\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mopenParams\u001b[39m(l): \n\u001b[1;32m    104\u001b[0m     x1,x2,x3,x4 \u001b[39m=\u001b[39m l\n\u001b[0;32m--> 105\u001b[0m     \u001b[39mreturn\u001b[39;00m And(x1(e),x2(u),Or(\u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(\u001b[39mlambda\u001b[39;00m x : x(a),x3))),Or(\u001b[39mtuple\u001b[39;49m(\u001b[39mmap\u001b[39;49m(\u001b[39mlambda\u001b[39;49;00m x : x(r),x4))))\n",
      "File \u001b[0;32m~/Dev/csc564Project/policy.py:105\u001b[0m, in \u001b[0;36musePolicyConstraints.<locals>.openParams.<locals>.<lambda>\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m    103\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mopenParams\u001b[39m(l): \n\u001b[1;32m    104\u001b[0m     x1,x2,x3,x4 \u001b[39m=\u001b[39m l\n\u001b[0;32m--> 105\u001b[0m     \u001b[39mreturn\u001b[39;00m And(x1(e),x2(u),Or(\u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(\u001b[39mlambda\u001b[39;00m x : x(a),x3))),Or(\u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(\u001b[39mlambda\u001b[39;00m x : x(r),x4))))\n",
      "File \u001b[0;32m~/Dev/csc564Project/policy.py:72\u001b[0m, in \u001b[0;36mconstructInRe.<locals>.<lambda>\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     71\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mconstructInRe\u001b[39m(n):\n\u001b[0;32m---> 72\u001b[0m     \u001b[39mreturn\u001b[39;00m \u001b[39mlambda\u001b[39;00m x: InRe(x, iam_pattern_to_regex(n))\n",
      "File \u001b[0;32m~/Dev/csc564Project/id_match.py:47\u001b[0m, in \u001b[0;36miam_pattern_to_regex\u001b[0;34m(pattern)\u001b[0m\n\u001b[1;32m     44\u001b[0m wildcard_regexes \u001b[39m=\u001b[39m \u001b[39mlist\u001b[39m(\u001b[39mmap\u001b[39m(to_wildcard, wildcards))\n\u001b[1;32m     46\u001b[0m \u001b[39m# a list of z3 regexes for the non-wildcard components\u001b[39;00m\n\u001b[0;32m---> 47\u001b[0m const_regexes \u001b[39m=\u001b[39m \u001b[39mlist\u001b[39;49m(\u001b[39mmap\u001b[39;49m(z3\u001b[39m.\u001b[39;49mRe, parts))\n\u001b[1;32m     49\u001b[0m \u001b[39m# we split the list into [non-wildcard, wildcard] chunks, and add them all together, padding with the empty regex.\u001b[39;00m\n\u001b[1;32m     50\u001b[0m \u001b[39m# even if a wildcard occurs at the beginning or end a string, i.e. \"*abcd\", re.split will add an extra ''\u001b[39;00m\n\u001b[1;32m     51\u001b[0m \u001b[39m# so we will always have a (maybe empty) non-wildcard string before the wildcard\u001b[39;00m\n\u001b[1;32m     52\u001b[0m regex_components \u001b[39m=\u001b[39m itertools\u001b[39m.\u001b[39mchain(\u001b[39m*\u001b[39m([part, wildcard] \u001b[39mfor\u001b[39;00m (part, wildcard) \u001b[39min\u001b[39;00m itertools\u001b[39m.\u001b[39mzip_longest(const_regexes, wildcard_regexes, fillvalue\u001b[39m=\u001b[39mz3\u001b[39m.\u001b[39mRe(\u001b[39m'\u001b[39m\u001b[39m'\u001b[39m))))\n",
      "File \u001b[0;32m~/Dev/csc564Project/env/lib/python3.10/site-packages/z3/z3.py:11114\u001b[0m, in \u001b[0;36mRe\u001b[0;34m(s, ctx)\u001b[0m\n\u001b[1;32m  11108\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mRe\u001b[39m(s, ctx\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m):\n\u001b[1;32m  11109\u001b[0m     \u001b[39m\"\"\"The regular expression that accepts sequence 's'\u001b[39;00m\n\u001b[1;32m  11110\u001b[0m \u001b[39m    >>> s1 = Re(\"ab\")\u001b[39;00m\n\u001b[1;32m  11111\u001b[0m \u001b[39m    >>> s2 = Re(StringVal(\"ab\"))\u001b[39;00m\n\u001b[1;32m  11112\u001b[0m \u001b[39m    >>> s3 = Re(Unit(BoolVal(True)))\u001b[39;00m\n\u001b[1;32m  11113\u001b[0m \u001b[39m    \"\"\"\u001b[39;00m\n\u001b[0;32m> 11114\u001b[0m     s \u001b[39m=\u001b[39m _coerce_seq(s, ctx)\n\u001b[1;32m  11115\u001b[0m     \u001b[39mreturn\u001b[39;00m ReRef(Z3_mk_seq_to_re(s\u001b[39m.\u001b[39mctx_ref(), s\u001b[39m.\u001b[39mas_ast()), s\u001b[39m.\u001b[39mctx)\n",
      "File \u001b[0;32m~/Dev/csc564Project/env/lib/python3.10/site-packages/z3/z3.py:10851\u001b[0m, in \u001b[0;36m_coerce_seq\u001b[0;34m(s, ctx)\u001b[0m\n\u001b[1;32m  10849\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39misinstance\u001b[39m(s, \u001b[39mstr\u001b[39m):\n\u001b[1;32m  10850\u001b[0m     ctx \u001b[39m=\u001b[39m _get_ctx(ctx)\n\u001b[0;32m> 10851\u001b[0m     s \u001b[39m=\u001b[39m StringVal(s, ctx)\n\u001b[1;32m  10852\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m is_expr(s):\n\u001b[1;32m  10853\u001b[0m     \u001b[39mraise\u001b[39;00m Z3Exception(\u001b[39m\"\u001b[39m\u001b[39mNon-expression passed as a sequence\u001b[39m\u001b[39m\"\u001b[39m)\n",
      "File \u001b[0;32m~/Dev/csc564Project/env/lib/python3.10/site-packages/z3/z3.py:10900\u001b[0m, in \u001b[0;36mStringVal\u001b[0;34m(s, ctx)\u001b[0m\n\u001b[1;32m  10898\u001b[0m s \u001b[39m=\u001b[39m \u001b[39m\"\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mjoin(\u001b[39mstr\u001b[39m(ch) \u001b[39mif\u001b[39;00m \u001b[39m32\u001b[39m \u001b[39m<\u001b[39m\u001b[39m=\u001b[39m \u001b[39mord\u001b[39m(ch) \u001b[39mand\u001b[39;00m \u001b[39mord\u001b[39m(ch) \u001b[39m<\u001b[39m \u001b[39m127\u001b[39m \u001b[39melse\u001b[39;00m \u001b[39m\"\u001b[39m\u001b[39m\\\\\u001b[39;00m\u001b[39mu\u001b[39m\u001b[39m{\u001b[39m\u001b[39m%x\u001b[39;00m\u001b[39m}\u001b[39m\u001b[39m\"\u001b[39m \u001b[39m%\u001b[39m (\u001b[39mord\u001b[39m(ch)) \u001b[39mfor\u001b[39;00m ch \u001b[39min\u001b[39;00m s)\n\u001b[1;32m  10899\u001b[0m ctx \u001b[39m=\u001b[39m _get_ctx(ctx)\n\u001b[0;32m> 10900\u001b[0m \u001b[39mreturn\u001b[39;00m SeqRef(Z3_mk_string(ctx\u001b[39m.\u001b[39;49mref(), s), ctx)\n",
      "File \u001b[0;32m~/Dev/csc564Project/env/lib/python3.10/site-packages/z3/z3.py:347\u001b[0m, in \u001b[0;36mAstRef.__init__\u001b[0;34m(self, ast, ctx)\u001b[0m\n\u001b[1;32m    345\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m__init__\u001b[39m(\u001b[39mself\u001b[39m, ast, ctx\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m):\n\u001b[1;32m    346\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mast \u001b[39m=\u001b[39m ast\n\u001b[0;32m--> 347\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mctx \u001b[39m=\u001b[39m _get_ctx(ctx)\n\u001b[1;32m    348\u001b[0m     Z3_inc_ref(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mctx\u001b[39m.\u001b[39mref(), \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mas_ast())\n",
      "File \u001b[0;32m~/Dev/csc564Project/env/lib/python3.10/site-packages/z3/z3.py:260\u001b[0m, in \u001b[0;36m_get_ctx\u001b[0;34m(ctx)\u001b[0m\n\u001b[1;32m    256\u001b[0m         _main_ctx \u001b[39m=\u001b[39m Context()\n\u001b[1;32m    257\u001b[0m     \u001b[39mreturn\u001b[39;00m _main_ctx\n\u001b[0;32m--> 260\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m_get_ctx\u001b[39m(ctx):\n\u001b[1;32m    261\u001b[0m     \u001b[39mif\u001b[39;00m ctx \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m    262\u001b[0m         \u001b[39mreturn\u001b[39;00m main_ctx()\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# test 1: 100 role groups, 100 users, vary path_length \n",
    "params1 = {\n",
    "    'num_role_groups': 100,\n",
    "    'roles_per_group': 4,\n",
    "    'role_branching_factor': 3,\n",
    "    'num_users': 100,\n",
    "    'max_n_objects': 4,\n",
    "    'max_n_actions': 3\n",
    "}\n",
    "\n",
    "branching_factors = [2*i for i in range(1, 20)]\n",
    "points = []\n",
    "path_lengths = []\n",
    "for n in branching_factors:\n",
    "    params1['role_branching_factor'] = n\n",
    "    r = perform_test(params1, n)\n",
    "    print(r)\n",
    "    if r['path_length'] not in path_lengths:\n",
    "        points.append(r['elapsed'])\n",
    "        path_lengths.append(r['path_length'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'plt' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[3], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m plt\u001b[39m.\u001b[39mxlabel(\u001b[39m'\u001b[39m\u001b[39mPath Length in Role Graph\u001b[39m\u001b[39m'\u001b[39m)\n\u001b[1;32m      2\u001b[0m plt\u001b[39m.\u001b[39mylabel(\u001b[39m'\u001b[39m\u001b[39mExecution Time (s)\u001b[39m\u001b[39m'\u001b[39m)\n\u001b[1;32m      3\u001b[0m plt\u001b[39m.\u001b[39mplot(\u001b[39msorted\u001b[39m(path_lengths), points)\n",
      "\u001b[0;31mNameError\u001b[0m: name 'plt' is not defined"
     ]
    }
   ],
   "source": [
    "plt.xlabel('Path Length in Role Graph')\n",
    "plt.ylabel('Execution Time (s)')\n",
    "plt.plot(sorted(path_lengths), points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arn:aws:iam::14354624986284130233:user/user_4\n",
      "s3:GetObjectAcl\n",
      "test_object_54747\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 10, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 10, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 3, 'num_roles': 21, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_4, s3:GetObjectAcl, test_object_54747)', 'elapsed': 0.506389604001015}\n",
      "arn:aws:iam::14354624986284130233:user/user_2\n",
      "s3:PutObject\n",
      "test_object_54865\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 20, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 20, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 5, 'num_roles': 43, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_2, s3:PutObject, test_object_54865)', 'elapsed': 0.17328534000080253}\n",
      "arn:aws:iam::14354624986284130233:user/user_28\n",
      "s3:InitiateReplication\n",
      "test_object_54982\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 30, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 30, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 5, 'num_roles': 62, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_28, s3:InitiateReplication, test_object_54982)', 'elapsed': 0.6034900269987702}\n",
      "arn:aws:iam::14354624986284130233:user/user_26\n",
      "s3:GetObject\n",
      "test_object_55239\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 40, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 40, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 98, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_26, s3:GetObject, test_object_55239)', 'elapsed': 0.3718258169992623}\n",
      "arn:aws:iam::14354624986284130233:user/user_21\n",
      "s3:PutObject\n",
      "test_object_55492\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 50, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 50, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 4, 'num_roles': 128, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_21, s3:PutObject, test_object_55492)', 'elapsed': 0.4853052109992859}\n",
      "arn:aws:iam::14354624986284130233:user/user_23\n",
      "s3:GetObject\n",
      "test_object_55887\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 60, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 60, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 144, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_23, s3:GetObject, test_object_55887)', 'elapsed': 0.6007223839988001}\n",
      "arn:aws:iam::14354624986284130233:user/user_48\n",
      "s3:DeleteObject\n",
      "test_object_56349\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 70, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 70, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 186, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_48, s3:DeleteObject, test_object_56349)', 'elapsed': 0.5969957399993291}\n",
      "arn:aws:iam::14354624986284130233:user/user_21\n",
      "s3:InitiateReplication\n",
      "test_object_56768\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 80, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 80, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 5, 'num_roles': 203, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_21, s3:InitiateReplication, test_object_56768)', 'elapsed': 0.5326282800015179}\n",
      "arn:aws:iam::14354624986284130233:user/user_60\n",
      "s3:DeleteObject\n",
      "test_object_57324\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 90, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 90, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 213, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_60, s3:DeleteObject, test_object_57324)', 'elapsed': 0.8263662749996001}\n",
      "arn:aws:iam::14354624986284130233:user/user_29\n",
      "s3:GetObject\n",
      "test_object_57991\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 261, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_29, s3:GetObject, test_object_57991)', 'elapsed': 0.7449024210000061}\n",
      "arn:aws:iam::14354624986284130233:user/user_57\n",
      "s3:DeleteObjectVersion\n",
      "test_object_58666\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 110, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 110, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 285, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_57, s3:DeleteObjectVersion, test_object_58666)', 'elapsed': 0.720185340000171}\n",
      "arn:aws:iam::14354624986284130233:user/user_63\n",
      "s3:DeleteObject\n",
      "test_object_59275\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 120, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 120, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 298, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_63, s3:DeleteObject, test_object_59275)', 'elapsed': 1.009496124999714}\n",
      "arn:aws:iam::14354624986284130233:user/user_102\n",
      "s3:GetObjectAcl\n",
      "test_object_60216\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 130, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 130, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 321, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_102, s3:GetObjectAcl, test_object_60216)', 'elapsed': 1.0758857410000928}\n",
      "arn:aws:iam::14354624986284130233:user/user_139\n",
      "s3:GetObject\n",
      "test_object_61002\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 140, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 140, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 377, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_139, s3:GetObject, test_object_61002)', 'elapsed': 1.2025567720011168}\n",
      "arn:aws:iam::14354624986284130233:user/user_116\n",
      "s3:GetObject\n",
      "test_object_62009\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 150, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 150, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 368, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_116, s3:GetObject, test_object_62009)', 'elapsed': 1.1008994029998576}\n",
      "arn:aws:iam::14354624986284130233:user/user_88\n",
      "s3:DeleteObject\n",
      "test_object_62481\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 160, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 160, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 5, 'num_roles': 398, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_88, s3:DeleteObject, test_object_62481)', 'elapsed': 1.325962442000673}\n",
      "arn:aws:iam::14354624986284130233:user/user_78\n",
      "s3:GetObjectRetention\n",
      "test_object_64065\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 170, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 170, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 450, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_78, s3:GetObjectRetention, test_object_64065)', 'elapsed': 1.8025600139990274}\n",
      "arn:aws:iam::14354624986284130233:user/user_59\n",
      "s3:DeleteObjectVersion\n",
      "test_object_65229\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 180, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 180, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 449, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_59, s3:DeleteObjectVersion, test_object_65229)', 'elapsed': 2.092796131000796}\n",
      "arn:aws:iam::14354624986284130233:user/user_133\n",
      "s3:DeleteObject\n",
      "test_object_66430\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 190, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 190, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 467, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_133, s3:DeleteObject, test_object_66430)', 'elapsed': 0.8205928610004776}\n",
      "arn:aws:iam::14354624986284130233:user/user_187\n",
      "s3:GetObjectRetention\n",
      "test_object_67470\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 200, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 200, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 491, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_187, s3:GetObjectRetention, test_object_67470)', 'elapsed': 2.8207975109999097}\n",
      "arn:aws:iam::14354624986284130233:user/user_10\n",
      "s3:GetObjectAcl\n",
      "test_object_68657\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 210, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 210, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 499, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_10, s3:GetObjectAcl, test_object_68657)', 'elapsed': 1.764160658000037}\n",
      "arn:aws:iam::14354624986284130233:user/user_36\n",
      "s3:InitiateReplication\n",
      "test_object_70127\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 220, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 220, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 550, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_36, s3:InitiateReplication, test_object_70127)', 'elapsed': 2.2491916969993326}\n",
      "arn:aws:iam::14354624986284130233:user/user_97\n",
      "s3:GetObjectRetention\n",
      "test_object_71465\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 230, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 230, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 547, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_97, s3:GetObjectRetention, test_object_71465)', 'elapsed': 2.8185344640005496}\n",
      "arn:aws:iam::14354624986284130233:user/user_61\n",
      "s3:GetObject\n",
      "test_object_72982\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 240, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 240, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 592, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_61, s3:GetObject, test_object_72982)', 'elapsed': 2.666747335999389}\n",
      "arn:aws:iam::14354624986284130233:user/user_223\n",
      "s3:GetObject\n",
      "test_object_74686\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 250, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 250, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 640, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_223, s3:GetObject, test_object_74686)', 'elapsed': 2.986961403999885}\n",
      "arn:aws:iam::14354624986284130233:user/user_81\n",
      "s3:PutObject\n",
      "test_object_75944\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 260, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 260, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 660, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_81, s3:PutObject, test_object_75944)', 'elapsed': 3.0019051909985137}\n",
      "arn:aws:iam::14354624986284130233:user/user_237\n",
      "s3:PutObject\n",
      "test_object_77811\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 270, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 270, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 677, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_237, s3:PutObject, test_object_77811)', 'elapsed': 5.454003601000295}\n",
      "arn:aws:iam::14354624986284130233:user/user_40\n",
      "s3:InitiateReplication\n",
      "test_object_79642\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 280, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 280, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 690, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_40, s3:InitiateReplication, test_object_79642)', 'elapsed': 3.680341944000247}\n",
      "arn:aws:iam::14354624986284130233:user/user_202\n",
      "s3:PutObject\n",
      "test_object_81294\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 290, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 290, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 759, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_202, s3:PutObject, test_object_81294)', 'elapsed': 4.285171065001123}\n",
      "arn:aws:iam::14354624986284130233:user/user_59\n",
      "s3:GetObject\n",
      "test_object_83461\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 300, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 300, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 765, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_59, s3:GetObject, test_object_83461)', 'elapsed': 4.133417469000051}\n",
      "arn:aws:iam::14354624986284130233:user/user_217\n",
      "s3:InitiateReplication\n",
      "test_object_85467\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 310, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 310, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 6, 'num_roles': 767, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_217, s3:InitiateReplication, test_object_85467)', 'elapsed': 4.012683983999523}\n",
      "arn:aws:iam::14354624986284130233:user/user_256\n",
      "s3:GetObject\n",
      "test_object_87013\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 320, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 320, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 825, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_256, s3:GetObject, test_object_87013)', 'elapsed': 5.28878976300075}\n",
      "arn:aws:iam::14354624986284130233:user/user_130\n",
      "s3:DeleteObject\n",
      "test_object_88915\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 330, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 330, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 825, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_130, s3:DeleteObject, test_object_88915)', 'elapsed': 4.562177132000215}\n",
      "arn:aws:iam::14354624986284130233:user/user_111\n",
      "s3:DeleteObject\n",
      "test_object_91696\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 340, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 340, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 845, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_111, s3:DeleteObject, test_object_91696)', 'elapsed': 7.572977737998372}\n",
      "arn:aws:iam::14354624986284130233:user/user_242\n",
      "s3:GetObjectRetention\n",
      "test_object_93844\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 350, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 350, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 906, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_242, s3:GetObjectRetention, test_object_93844)', 'elapsed': 5.722103428999617}\n",
      "arn:aws:iam::14354624986284130233:user/user_183\n",
      "s3:PutObject\n",
      "test_object_95671\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 360, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 360, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 899, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_183, s3:PutObject, test_object_95671)', 'elapsed': 7.205233734999638}\n",
      "arn:aws:iam::14354624986284130233:user/user_135\n",
      "s3:PutObject\n",
      "test_object_98544\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 370, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 370, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 963, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_135, s3:PutObject, test_object_98544)', 'elapsed': 6.539846231000411}\n",
      "arn:aws:iam::14354624986284130233:user/user_314\n",
      "s3:GetObject\n",
      "test_object_100811\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 380, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 380, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 923, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_314, s3:GetObject, test_object_100811)', 'elapsed': 9.92272224000044}\n",
      "arn:aws:iam::14354624986284130233:user/user_7\n",
      "s3:InitiateReplication\n",
      "test_object_102807\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 390, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 390, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 950, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_7, s3:InitiateReplication, test_object_102807)', 'elapsed': 10.002669622001122}\n",
      "arn:aws:iam::14354624986284130233:user/user_292\n",
      "s3:InitiateReplication\n",
      "test_object_105573\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 400, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 400, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 1040, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_292, s3:InitiateReplication, test_object_105573)', 'elapsed': 10.504037630998937}\n",
      "arn:aws:iam::14354624986284130233:user/user_369\n",
      "s3:DeleteObjectVersion\n",
      "test_object_108107\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 410, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 410, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 994, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_369, s3:DeleteObjectVersion, test_object_108107)', 'elapsed': 8.312356409000131}\n",
      "arn:aws:iam::14354624986284130233:user/user_285\n",
      "s3:GetObjectRetention\n",
      "test_object_110802\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 420, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 420, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 1028, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_285, s3:GetObjectRetention, test_object_110802)', 'elapsed': 6.392430392999813}\n",
      "arn:aws:iam::14354624986284130233:user/user_178\n",
      "s3:DeleteObjectVersion\n",
      "test_object_113236\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 430, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 430, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 1064, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_178, s3:DeleteObjectVersion, test_object_113236)', 'elapsed': 9.005452735998915}\n",
      "arn:aws:iam::14354624986284130233:user/user_179\n",
      "s3:InitiateReplication\n",
      "test_object_116170\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 440, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 440, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 1059, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_179, s3:InitiateReplication, test_object_116170)', 'elapsed': 10.353992820999338}\n",
      "arn:aws:iam::14354624986284130233:user/user_13\n",
      "s3:GetObject\n",
      "test_object_118602\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 450, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 450, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 9, 'num_roles': 1131, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_13, s3:GetObject, test_object_118602)', 'elapsed': 8.764639441998952}\n",
      "arn:aws:iam::14354624986284130233:user/user_451\n",
      "s3:DeleteObjectVersion\n",
      "test_object_121781\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 460, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 460, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 10, 'num_roles': 1141, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_451, s3:DeleteObjectVersion, test_object_121781)', 'elapsed': 10.977717558000222}\n",
      "arn:aws:iam::14354624986284130233:user/user_20\n",
      "sts:AssumeRole\n",
      "arn:aws:iam::14354624986284130233:role/role_r456_4\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 470, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 470, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 1161, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_20, sts:AssumeRole, arn:aws:iam::14354624986284130233:role/role_r456_4)', 'elapsed': 30.577910236001117}\n",
      "arn:aws:iam::14354624986284130233:user/user_403\n",
      "s3:DeleteObject\n",
      "test_object_127457\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 480, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 480, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 8, 'num_roles': 1200, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_403, s3:DeleteObject, test_object_127457)', 'elapsed': 13.009938555998815}\n",
      "arn:aws:iam::14354624986284130233:user/user_311\n",
      "s3:DeleteObject\n",
      "test_object_130583\n",
      "sat\n",
      "{'result': False, 'params': {'num_role_groups': 490, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 490, 'max_n_objects': 4, 'max_n_actions': 3}, 'path_length': 7, 'num_roles': 1154, 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_311, s3:DeleteObject, test_object_130583)', 'elapsed': 10.468568500000401}\n"
     ]
    }
   ],
   "source": [
    "# test 2: vary users and number of role groups (i.e., number of roles ~= k*n_users)\n",
    "params2 = {\n",
    "    'num_role_groups': 100,\n",
    "    'roles_per_group': 4,\n",
    "    'role_branching_factor': 3,\n",
    "    'num_users': 100,\n",
    "    'max_n_objects': 4,\n",
    "    'max_n_actions': 3\n",
    "}\n",
    "\n",
    "sizes = [10*i for i in range(1, 50)]\n",
    "points = []\n",
    "for n in sizes:\n",
    "    params2['num_users'] = n\n",
    "    params2['num_role_groups'] = n\n",
    "    r = perform_test(params2, n)\n",
    "    print(r)\n",
    "    points.append(r['elapsed'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1234300a0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Number of Users/Role Groups')\n",
    "plt.ylabel('Execution Time (s)')\n",
    "plt.plot(sizes, points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "params7 = {\n",
    "    'num_role_groups': 80,\n",
    "    'roles_per_group': 4,\n",
    "    'role_branching_factor': 3,\n",
    "    'num_users': 240,\n",
    "    'max_n_objects': 4,\n",
    "    'max_n_actions': 3\n",
    "}\n",
    "\n",
    "params8 = {\n",
    "    'num_role_groups': 160,\n",
    "    'roles_per_group': 4,\n",
    "    'role_branching_factor': 3,\n",
    "    'num_users': 480,\n",
    "    'max_n_objects': 4,\n",
    "    'max_n_actions': 3\n",
    "}\n",
    "\n",
    "params9 = {\n",
    "    'num_role_groups': 320,\n",
    "    'roles_per_group': 4,\n",
    "    'role_branching_factor': 3,\n",
    "    'num_users': 960,\n",
    "    'max_n_objects': 4,\n",
    "    'max_n_actions': 3\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arn:aws:iam::14354624986284130233:user/user_63\n",
      "s3:DeleteObject\n",
      "test_object_48934\n",
      "sat\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'result': False,\n",
       " 'params': {'num_role_groups': 80,\n",
       "  'roles_per_group': 4,\n",
       "  'role_branching_factor': 3,\n",
       "  'num_users': 240,\n",
       "  'max_n_objects': 4,\n",
       "  'max_n_actions': 3},\n",
       " 'path_length': 7,\n",
       " 'num_roles': 206,\n",
       " 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_63, s3:DeleteObject, test_object_48934)',\n",
       " 'elapsed': 20.941573382999195}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perform_test(params7, id=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arn:aws:iam::14354624986284130233:user/user_137\n",
      "s3:GetObjectRetention\n",
      "test_object_5828\n",
      "sat\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'result': False,\n",
       " 'params': {'num_role_groups': 320,\n",
       "  'roles_per_group': 4,\n",
       "  'role_branching_factor': 3,\n",
       "  'num_users': 960,\n",
       "  'max_n_objects': 4,\n",
       "  'max_n_actions': 3},\n",
       " 'path_length': 9,\n",
       " 'num_roles': 784,\n",
       " 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_137, s3:GetObjectRetention, test_object_5828)',\n",
       " 'elapsed': 115.57802481300018}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perform_test(params9, id=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arn:aws:iam::14354624986284130233:user/user_164\n",
      "s3:GetObjectRetention\n",
      "test_object_52004\n",
      "sat\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'result': False,\n",
       " 'params': {'num_role_groups': 160,\n",
       "  'roles_per_group': 4,\n",
       "  'role_branching_factor': 3,\n",
       "  'num_users': 480,\n",
       "  'max_n_objects': 4,\n",
       "  'max_n_actions': 3},\n",
       " 'path_length': 9,\n",
       " 'num_roles': 426,\n",
       " 'q': 'Allow(arn:aws:iam::14354624986284130233:user/user_164, s3:GetObjectRetention, test_object_52004)',\n",
       " 'elapsed': 30.273361627998383}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "perform_test(params8, id=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 10, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 10, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 16, 'avg_elapsed': 0.09093979109929932}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 20, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 20, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 60, 'avg_elapsed': 0.11363584390019241}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 30, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 30, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 81, 'avg_elapsed': 0.2232736482994369}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 40, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 40, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 104, 'avg_elapsed': 0.165665681199971}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 50, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 50, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 142, 'avg_elapsed': 0.5095305655999255}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 60, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 60, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 144, 'avg_elapsed': 0.5664169975996629}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 70, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 70, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 180, 'avg_elapsed': 0.3535040050999669}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 80, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 80, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 201, 'avg_elapsed': 0.42389484379964415}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 90, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 90, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 218, 'avg_elapsed': 0.4679946268995991}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 100, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 100, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 250, 'avg_elapsed': 2.0337869123002745}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 110, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 110, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 291, 'avg_elapsed': 0.5644845737995638}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 120, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 120, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 304, 'avg_elapsed': 0.6725353405996429}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 130, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 130, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 329, 'avg_elapsed': 1.539053193199652}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 140, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 140, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 342, 'avg_elapsed': 0.9289088790006644}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 150, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 150, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 368, 'avg_elapsed': 2.7996167196997703}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 160, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 160, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 422, 'avg_elapsed': 2.913765759000307}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 170, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 170, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 432, 'avg_elapsed': 1.191331229399657}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 180, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 180, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 462, 'avg_elapsed': 5.235081839600388}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 190, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 190, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 496, 'avg_elapsed': 1.4920993332998478}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 200, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 200, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 509, 'avg_elapsed': 5.983645982100279}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 210, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 210, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 529, 'avg_elapsed': 1.5960720032995597}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 220, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 220, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 555, 'avg_elapsed': 4.036536864799928}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 230, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 230, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 580, 'avg_elapsed': 5.058390029800648}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 240, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 240, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 559, 'avg_elapsed': 3.7083924066999314}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 250, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 250, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 662, 'avg_elapsed': 2.557241495400376}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 260, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 260, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 663, 'avg_elapsed': 9.637822568299816}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 270, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 270, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 656, 'avg_elapsed': 13.894040209599916}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 280, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 280, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 716, 'avg_elapsed': 15.806020827800603}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 290, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 290, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 737, 'avg_elapsed': 8.912753916300062}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 300, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 300, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 787, 'avg_elapsed': 15.104217922799581}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 310, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 310, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 799, 'avg_elapsed': 3.9029127737005185}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 320, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 320, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 802, 'avg_elapsed': 15.596832986900335}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 330, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 330, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 822, 'avg_elapsed': 19.51682314069949}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 340, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 340, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 838, 'avg_elapsed': 13.708628972899533}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 350, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 350, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 837, 'avg_elapsed': 18.661591517000126}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 360, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 360, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 905, 'avg_elapsed': 5.062319033900349}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 370, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 370, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 909, 'avg_elapsed': 12.196286186399812}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 380, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 380, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 937, 'avg_elapsed': 26.00687389379964}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 390, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 390, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 994, 'avg_elapsed': 25.597801702099968}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 400, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 400, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 992, 'avg_elapsed': 19.65244620230005}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 410, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 410, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1040, 'avg_elapsed': 8.98541278670018}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 420, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 420, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1066, 'avg_elapsed': 9.548413383000298}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 430, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 430, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1093, 'avg_elapsed': 25.320940585400603}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 440, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 440, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1089, 'avg_elapsed': 31.499231278599837}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 450, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 450, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1154, 'avg_elapsed': 39.15685778709958}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 460, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 460, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1119, 'avg_elapsed': 10.005487941800675}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 470, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 470, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1135, 'avg_elapsed': 48.374705664700016}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 480, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 480, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1199, 'avg_elapsed': 22.98558311370034}\n",
      "{'result': [sat, sat, sat, sat, sat, sat, sat, sat, sat, sat], 'params': {'num_role_groups': 490, 'roles_per_group': 4, 'role_branching_factor': 3, 'num_users': 490, 'max_n_objects': 4, 'max_n_actions': 3}, 'num_roles': 1220, 'avg_elapsed': 32.91964218800094}\n"
     ]
    }
   ],
   "source": [
    "params3 = {\n",
    "    'num_role_groups': 100,\n",
    "    'roles_per_group': 4,\n",
    "    'role_branching_factor': 3,\n",
    "    'num_users': 100,\n",
    "    'max_n_objects': 4,\n",
    "    'max_n_actions': 3\n",
    "}\n",
    "\n",
    "sizes = [10*i for i in range(1, 50)]\n",
    "avg_elapsed = []\n",
    "for n in sizes:\n",
    "    params3['num_users'] = n\n",
    "    params3['num_role_groups'] = n\n",
    "    r = perform_averaged_test(params3)\n",
    "    print(r)\n",
    "    avg_elapsed.append(r['avg_elapsed'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10f966d70>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Number of Users/Role Groups')\n",
    "plt.ylabel('Average Access Time (s)')\n",
    "plt.plot(sizes, avg_elapsed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import random\n",
    "\n",
    "dg = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 5)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def rand_walk(dg, k):\n",
    "    v = random.choice(list(dg.nodes))\n",
    "    seen = 0\n",
    "    path = []\n",
    "    while seen < k:\n",
    "        seen += 1\n",
    "        path.append(v)\n",
    "        if len(dg[v]) == 0:\n",
    "            break\n",
    "        else:\n",
    "            v = random.choice(list(dg[v]))\n",
    "    \n",
    "    return path\n",
    "\n",
    "rand_walk(dg, 2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.1 ('env': venv)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.1"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "de07810760c49f6365e5a6393fc4630e7887d47cff617a62870208914051d748"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}