performance_and_time.ipynb

{
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  {
   "cell_type": "code",
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   "source": [
    "import time\n",
    "from itertools import product\n",
    "\n",
    "import altair as alt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import torch\n",
    "from numba import njit, bool_\n",
    "from prettytable import PrettyTable\n",
    "from torch_geometric.loader import DataLoader\n",
    "\n",
    "from loss import create_loss_fn\n",
    "from model import FlexNet\n",
    "from utils.algorithms import get_directional_sum_rate, wmmse\n",
    "from utils.data import flex_graph, gen_rectangular_channel_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "# Data generation functions\n",
    "def generate_data(n, k):\n",
    "    return gen_rectangular_channel_matrix(k, k, n, seed=899)\n",
    "\n",
    "\n",
    "# GNN evaluation\n",
    "def load_model(path):\n",
    "    model = FlexNet()\n",
    "    model.load_state_dict(torch.load(path, map_location=torch.device('cpu')))\n",
    "    model.eval()\n",
    "    return model\n",
    "\n",
    "\n",
    "def eval_model(model, data):\n",
    "    k = data.shape[-1]\n",
    "    data = flex_graph(data)\n",
    "    data = next(iter(DataLoader(data, batch_size=data.size, shuffle=False)))\n",
    "    outs = model(data)\n",
    "    p, t = outs\n",
    "    t = torch.where(t >= 0.5, 1., 0.)\n",
    "    p = torch.where(p >= 0.5, 1., 0.)\n",
    "    return p, t, data\n",
    "\n",
    "\n",
    "# Exhaustive search related functions\n",
    "@njit\n",
    "def find_best_sum_rate(h, directions):\n",
    "    k = np.shape(h)[-1]\n",
    "    sum_rate = 0.\n",
    "    # best_p = None\n",
    "    # best_t = None\n",
    "    for direction in directions:\n",
    "        t = np.vstack((direction, 1 - direction)).T.ravel()\n",
    "        p = wmmse(np.ones(int(k / 2)), get_h(h, t), 1., 1.)\n",
    "        p_hat = np.zeros(k)\n",
    "        for j in range(k):\n",
    "            if t[j] == 1:\n",
    "                p_hat[j] = p[0]\n",
    "                p = p[1:]\n",
    "        new_sum = get_directional_sum_rate(h, p_hat, t, 1., k)\n",
    "        if new_sum >= sum_rate:\n",
    "            sum_rate = new_sum\n",
    "    return sum_rate\n",
    "\n",
    "\n",
    "@njit\n",
    "def get_h(h, t):\n",
    "    return h[:, (1 - t).astype(bool_)][t.astype(bool_), :]\n",
    "\n",
    "\n",
    "def get_direction_combinations(k):\n",
    "    return np.array(list(product([0., 1.], repeat=k)), dtype=np.float32)\n",
    "\n",
    "\n",
    "# Heuristic search related functions\n",
    "@njit\n",
    "def find_best_pat(h):\n",
    "    k = np.shape(h)[-1]\n",
    "    p = np.ones(k)\n",
    "    prev_rate = 0.\n",
    "    for i in range(100):\n",
    "        _, t = pattern_search2(h, p, k)\n",
    "        p_wmmse = wmmse(np.ones(int(k / 2)), get_h(h, t), 1., 1.)\n",
    "        p_hat = np.zeros(k)\n",
    "        p_hat_mask = np.ones(k, dtype=bool_)\n",
    "        for j in range(k):\n",
    "            if t[j] == 1:\n",
    "                p_hat[j] = p_wmmse[0]\n",
    "                p_wmmse = p_wmmse[1:]\n",
    "        p = p_hat.copy()\n",
    "        sum_rate = get_directional_sum_rate(h, p, t, 1., k)\n",
    "        if sum_rate - prev_rate <= 1e-6:\n",
    "            break\n",
    "        prev_rate = sum_rate\n",
    "    return sum_rate\n",
    "\n",
    "\n",
    "@njit\n",
    "def build_t_vec(t):\n",
    "    return np.vstack((t, 1 - t)).T.ravel()\n",
    "\n",
    "\n",
    "@njit\n",
    "def pattern_search2(h, p, k):\n",
    "    num_of_pairs = int(k / 2)\n",
    "    max_rate = np.empty(num_of_pairs + 1)\n",
    "    max_t = np.empty((num_of_pairs + 1, k))\n",
    "    t_pattern = np.zeros((num_of_pairs + 1, num_of_pairs))\n",
    "    for i in range(0, num_of_pairs):\n",
    "        t_pattern[i + 1][i] = 1\n",
    "    for j, pat in enumerate(t_pattern):\n",
    "        max_idx = j\n",
    "        t_pat = pat.copy()\n",
    "        while True:\n",
    "            sum_rates = np.empty(num_of_pairs + 1)\n",
    "            sum_rates[0] = get_directional_sum_rate(h, p, build_t_vec(t_pat), 1., k)\n",
    "            for i in range(num_of_pairs):\n",
    "                t = t_pat.copy()\n",
    "                t[i] = 1\n",
    "                sum_rates[i + 1] = get_directional_sum_rate(h, p, build_t_vec(t), 1., k)\n",
    "            index = np.argmax(sum_rates)\n",
    "            if index == 0 or index == max_idx:\n",
    "                break\n",
    "            else:\n",
    "                t_pat[index - 1] = 1\n",
    "                max_idx = index\n",
    "        max_rate[j] = get_directional_sum_rate(h, p, build_t_vec(t_pat), 1., k)\n",
    "        max_t[j] = build_t_vec(t_pat)\n",
    "    max_rate_idx = np.argmax(max_rate)\n",
    "    return max_rate[max_rate_idx], max_t[max_rate_idx]\n",
    "\n",
    "\n",
    "# max channel\n",
    "@njit\n",
    "def wmmse_with_max_channel(h):\n",
    "    k = np.shape(h)[-1]\n",
    "    t = max_channel(h)\n",
    "    p = wmmse(np.ones(int(k / 2)), get_h(h, t), 1., 1.)\n",
    "    p_hat = np.zeros(k)\n",
    "    for j in range(k):\n",
    "        if t[j] == 1:\n",
    "            p_hat[j] = p[0]\n",
    "            p = p[1:]\n",
    "    return p_hat, t\n",
    "\n",
    "\n",
    "@njit\n",
    "def max_channel(h):\n",
    "    k = np.shape(h)[-1]\n",
    "    d = np.ones(int(k / 2))\n",
    "    d_k = np.vstack((d, 1 - d)).T.ravel()\n",
    "    left_ro_right = np.diag(get_h(h, d_k))\n",
    "    right_to_left = np.diag(get_h(h, 1 - d_k))\n",
    "    t = np.zeros((2, int(k / 2)))\n",
    "    for i in range(int(k / 2)):\n",
    "        if left_ro_right[i] >= right_to_left[i]:\n",
    "            t[0, i] = 1.\n",
    "        else:\n",
    "            t[1, i] = 1.\n",
    "    t = t.T.ravel()\n",
    "    return t\n",
    "\n",
    "\n",
    "@njit\n",
    "def find_average_rate(h, algorithm, *args):\n",
    "    avg_rate = 0.\n",
    "    for mat in h:\n",
    "        avg_rate += algorithm(mat, *args)\n",
    "    return avg_rate / np.shape(h)[0]\n",
    "\n",
    "\n",
    "@njit\n",
    "def get_max_directions(h):\n",
    "    n = np.shape(h)[0]\n",
    "    k = np.shape(h)[-1]\n",
    "    max_directions = np.empty((n, k))\n",
    "    for i in range(n):\n",
    "        max_directions[i] = max_channel(h[i])\n",
    "    return max_directions\n",
    "\n",
    "\n",
    "@njit\n",
    "def get_max_dir_with_power(h):\n",
    "    n = np.shape(h)[0]\n",
    "    k = np.shape(h)[-1]\n",
    "    max_directions = np.empty((n, k))\n",
    "    power = np.empty((n, k))\n",
    "    for i in range(n):\n",
    "        power[i], max_directions[i] = wmmse_with_max_channel(h[i])\n",
    "    return power, max_directions\n",
    "\n",
    "\n",
    "@njit\n",
    "def calculate_rates_and_average(h, p, t):\n",
    "    n = np.shape(h)[0]\n",
    "    k = np.shape(h)[-1]\n",
    "    sum_rate = 0.\n",
    "    for i in range(n):\n",
    "        sum_rate += get_directional_sum_rate(h[i], p[i], t[i], 1., k)\n",
    "    return sum_rate / n\n",
    "\n",
    "\n",
    "def time_code(func, *args):\n",
    "    start = time.perf_counter()\n",
    "    result = func(*args)\n",
    "    end = time.perf_counter()\n",
    "    return end - start, result\n",
    "\n",
    "\n",
    "def format_float(number):\n",
    "    return f'{number:.4f}'"
   ],
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   "execution_count": 3,
   "outputs": [],
   "source": [
    "def evaluate_algorithms(h):\n",
    "    n = h.shape[0]\n",
    "    k = h.shape[-1]\n",
    "    results = {}\n",
    "    table = PrettyTable()\n",
    "    table.field_names = ['Algorithm', 'Time', 'Performance']\n",
    "\n",
    "    find_average_rate(h[:1, :, :], find_best_pat)\n",
    "    time_heuristic, rate_heuristic = time_code(find_average_rate, h, find_best_pat)\n",
    "    results['heuristic'] = (time_heuristic / n, rate_heuristic)\n",
    "    table.add_row(['Heuristic Search', format_float(time_heuristic / n), format_float(rate_heuristic)])\n",
    "\n",
    "    dirs = get_direction_combinations(int(h.shape[-1] / 2))\n",
    "    find_average_rate(h[:1, :, :], find_best_sum_rate, dirs)\n",
    "    time_exhaustive, rate_exhaustive = time_code(find_average_rate, h, find_best_sum_rate, dirs)\n",
    "    results['exhaustive'] = (time_exhaustive / n, rate_exhaustive)\n",
    "    # results['exhaustive'] = (0., 0.)\n",
    "    table.add_row(['Exhaustive Search', format_float(time_exhaustive / n), format_float(rate_exhaustive)])\n",
    "\n",
    "    get_max_directions(h[:1, :, :])\n",
    "    time_max_channel, max_directions = time_code(get_max_directions, h)\n",
    "    rate_max_direction = calculate_rates_and_average(h, np.ones((n, k)), max_directions)\n",
    "    results['max_power'] = (time_max_channel / n, rate_max_direction)\n",
    "    table.add_row(['Max Power', format_float(time_max_channel / n), format_float(rate_max_direction)])\n",
    "\n",
    "    get_max_dir_with_power(h[:1, :, :])\n",
    "    time_wmmse, (p_wmmse, d_wmmse) = time_code(get_max_dir_with_power, h)\n",
    "    rate_wmmse = calculate_rates_and_average(h, p_wmmse, d_wmmse)\n",
    "    results['wmmse_max'] = (time_wmmse / n, rate_wmmse)\n",
    "    table.add_row(['WMMSE with max channel', format_float(time_wmmse / n), format_float(rate_wmmse)])\n",
    "\n",
    "    path_ = f'./experiments/flexible_experiment_{h.shape[-1]}_nodes.pth'\n",
    "    model = load_model(path_)\n",
    "    eval_model(model, h[:1, :, :])\n",
    "    time_gnn, (p, t, data) = time_code(eval_model, model, h)\n",
    "    rate = create_loss_fn(h.shape[-1], 1.)\n",
    "    rate_gnn = -rate((p, t), data.y).item()\n",
    "    results['gnn'] = (time_gnn / n, rate_gnn)\n",
    "    table.add_row(['Flex-Net', format_float(time_gnn / n), format_float(rate_gnn)])\n",
    "\n",
    "    print('\\n', h.shape[-1], '\\033[1m' + '- nodes' + '\\033[0m')\n",
    "    print(table)\n",
    "    return results\n",
    "\n",
    "\n",
    "def evaluate_and_save_results():\n",
    "    nodes = [4, 8, 12, 16, 20, 24, 28, 32]\n",
    "    df = pd.DataFrame(\n",
    "        columns=[\n",
    "            'Nodes',\n",
    "            'GNN Time',\n",
    "            'GNN Performance',\n",
    "            'Heuristic Time',\n",
    "            'Heuristic Performance',\n",
    "            'Exhaustive Time',\n",
    "            'Exhaustive Performance',\n",
    "            'Max Power Time',\n",
    "            'Max Power Performance',\n",
    "            'WMMSE with Max Power Time',\n",
    "            'WMMSE with Max Power Performance',\n",
    "        ])\n",
    "    for i, val in enumerate(nodes):\n",
    "        channel_data = generate_data(10, val)\n",
    "        results = evaluate_algorithms(channel_data)\n",
    "        df.loc[i] = [val] + list(results['gnn']) + list(results['heuristic']) + list(results['exhaustive']) + \\\n",
    "                    list(results['max_power']) + list(results['wmmse_max'])\n",
    "\n",
    "    df.to_pickle('./experiments/perf_summary.pkl')\n",
    "\n",
    "\n",
    "def plot_results():\n",
    "    df = pd.read_pickle('./experiments/perf_summary.pkl')\n",
    "    pd.options.display.max_columns = None\n",
    "    pd.options.display.max_rows = None\n",
    "    print(df.head(10))\n",
    "    source_perf = df[\n",
    "        ['Nodes', 'GNN Performance', 'Heuristic Performance', 'Exhaustive Performance', 'Max Power Performance',\n",
    "         'WMMSE with Max Power Performance']] \\\n",
    "        .melt('Nodes',\n",
    "              var_name='category',\n",
    "              value_name='Performance')\n",
    "\n",
    "    chart_perf = alt.Chart(source_perf).mark_line(point=True, interpolate='monotone').configure_point(\n",
    "        size=50\n",
    "    ).transform_joinaggregate(\n",
    "        max='max(Performance)',\n",
    "    ).transform_calculate(\n",
    "        percent=\"datum.Performance / datum.max\"\n",
    "    ).encode(\n",
    "        alt.X('Nodes:O', scale=alt.Scale(zero=False)),\n",
    "        alt.Y('percent:Q', title='Performance', scale=alt.Scale(zero=False), axis=alt.Axis(format='.1%')),\n",
    "        alt.Color('category:N',\n",
    "                  legend=alt.Legend(orient='top-left', title=None),\n",
    "                  scale=alt.Scale(scheme=\"dark2\")),\n",
    "    ).properties(\n",
    "        width=400\n",
    "    )\n",
    "\n",
    "    source_time = df[['Nodes', 'GNN Time', 'Heuristic Time', 'Exhaustive Time', 'Max Power Time',\n",
    "                      'WMMSE with Max Power Time']] \\\n",
    "        .melt('Nodes',\n",
    "              var_name='category',\n",
    "              value_name='Time')\n",
    "\n",
    "    chart_time = alt.Chart(source_time).mark_line(point=True, interpolate='monotone').configure_point(\n",
    "        size=50\n",
    "    ).encode(\n",
    "        alt.X('Nodes:O', scale=alt.Scale(zero=False), axis=alt.Axis(tickCount=8)),\n",
    "        alt.Y('Time:Q', title='Time (s)', scale=alt.Scale(type='log')),\n",
    "        alt.Color('category:N',\n",
    "                  legend=alt.Legend(orient='top-left', title=None),\n",
    "                  scale=alt.Scale(scheme=\"dark2\")),\n",
    "    ).properties(\n",
    "        width=400\n",
    "    )\n",
    "    return chart_perf, chart_time"
   ],
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  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "# evaluate_and_save_results()"
   ],
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    "pycharm": {
     "name": "#%%\n"
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   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Nodes  GNN Time  GNN Performance  Heuristic Time  Heuristic Performance  \\\n",
      "0    4.0  0.000229         1.791022        0.000113               1.771709   \n",
      "1    8.0  0.000251         2.495414        0.000550               2.460771   \n",
      "2   12.0  0.000283         2.920749        0.001467               2.884021   \n",
      "3   16.0  0.000343         3.265862        0.003362               3.225337   \n",
      "4   20.0  0.000401         3.519804        0.006781               3.489375   \n",
      "5   24.0  0.000491         3.745244        0.012289               3.707267   \n",
      "6   28.0  0.000552         3.931401        0.022320               3.901677   \n",
      "7   32.0  0.000710         4.091971        0.037172               4.076983   \n",
      "\n",
      "   Exhaustive Time  Exhaustive Performance  Max Power Time  \\\n",
      "0         0.000030                1.798028        0.000002   \n",
      "1         0.000282                2.548500        0.000003   \n",
      "2         0.001931                3.004615        0.000003   \n",
      "3         0.012367                3.366040        0.000003   \n",
      "4         0.070945                3.648055        0.000003   \n",
      "5         0.396781                3.879088        0.000004   \n",
      "6         2.130370                4.082910        0.000004   \n",
      "7        11.687468                4.267732        0.000004   \n",
      "\n",
      "   Max Power Performance  WMMSE with Max Power Time  \\\n",
      "0               1.647709                   0.000006   \n",
      "1               1.959575                   0.000016   \n",
      "2               2.030862                   0.000032   \n",
      "3               2.086981                   0.000052   \n",
      "4               2.098115                   0.000074   \n",
      "5               2.111427                   0.000107   \n",
      "6               2.122792                   0.000142   \n",
      "7               2.132915                   0.000195   \n",
      "\n",
      "   WMMSE with Max Power Performance  \n",
      "0                          1.729876  \n",
      "1                          2.418558  \n",
      "2                          2.841115  \n",
      "3                          3.181837  \n",
      "4                          3.444680  \n",
      "5                          3.663508  \n",
      "6                          3.851553  \n",
      "7                          4.025108  \n"
     ]
    }
   ],
   "source": [
    "chart_perf, chart_time = plot_results()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
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3.519803524017334}, {\"Nodes\": 24.0, \"category\": \"GNN Performance\", \"Performance\": 3.745243787765503}, {\"Nodes\": 28.0, \"category\": \"GNN Performance\", \"Performance\": 3.931401491165161}, {\"Nodes\": 32.0, \"category\": \"GNN Performance\", \"Performance\": 4.091970920562744}, {\"Nodes\": 4.0, \"category\": \"Heuristic Performance\", \"Performance\": 1.7717088949672266}, {\"Nodes\": 8.0, \"category\": \"Heuristic Performance\", \"Performance\": 2.4607712576358516}, {\"Nodes\": 12.0, \"category\": \"Heuristic Performance\", \"Performance\": 2.884021408324024}, {\"Nodes\": 16.0, \"category\": \"Heuristic Performance\", \"Performance\": 3.2253373891256683}, {\"Nodes\": 20.0, \"category\": \"Heuristic Performance\", \"Performance\": 3.489375304403542}, {\"Nodes\": 24.0, \"category\": \"Heuristic Performance\", \"Performance\": 3.707267275573535}, {\"Nodes\": 28.0, \"category\": \"Heuristic Performance\", \"Performance\": 3.9016767751794665}, {\"Nodes\": 32.0, \"category\": \"Heuristic Performance\", \"Performance\": 4.076983221155659}, {\"Nodes\": 4.0, \"category\": \"Exhaustive Performance\", \"Performance\": 1.7980275802419687}, {\"Nodes\": 8.0, \"category\": \"Exhaustive Performance\", \"Performance\": 2.5484998107757812}, {\"Nodes\": 12.0, \"category\": \"Exhaustive Performance\", \"Performance\": 3.004614687149399}, {\"Nodes\": 16.0, \"category\": \"Exhaustive Performance\", \"Performance\": 3.3660403597442747}, {\"Nodes\": 20.0, \"category\": \"Exhaustive Performance\", \"Performance\": 3.648055391196141}, {\"Nodes\": 24.0, \"category\": \"Exhaustive Performance\", \"Performance\": 3.879088411289332}, {\"Nodes\": 28.0, \"category\": \"Exhaustive Performance\", \"Performance\": 4.082909639219558}, {\"Nodes\": 32.0, \"category\": \"Exhaustive Performance\", \"Performance\": 4.267731541080399}, {\"Nodes\": 4.0, \"category\": \"Max Power Performance\", \"Performance\": 1.6477086106196182}, {\"Nodes\": 8.0, \"category\": \"Max Power Performance\", \"Performance\": 1.9595749936062434}, {\"Nodes\": 12.0, \"category\": \"Max Power Performance\", \"Performance\": 2.030862074274379}, {\"Nodes\": 16.0, \"category\": \"Max Power Performance\", \"Performance\": 2.0869810874424783}, {\"Nodes\": 20.0, \"category\": \"Max Power Performance\", \"Performance\": 2.0981147231891164}, {\"Nodes\": 24.0, \"category\": \"Max Power Performance\", \"Performance\": 2.111426518520623}, {\"Nodes\": 28.0, \"category\": \"Max Power Performance\", \"Performance\": 2.122791772747697}, {\"Nodes\": 32.0, \"category\": \"Max Power Performance\", \"Performance\": 2.132915332424665}, {\"Nodes\": 4.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 1.7298758191166737}, {\"Nodes\": 8.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 2.4185579859706836}, {\"Nodes\": 12.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 2.8411150824983866}, {\"Nodes\": 16.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 3.1818372884308497}, {\"Nodes\": 20.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 3.444680138527434}, {\"Nodes\": 24.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 3.663508274594987}, {\"Nodes\": 28.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 3.851553182308157}, {\"Nodes\": 32.0, \"category\": \"WMMSE with Max Power Performance\", \"Performance\": 4.0251082417535144}]}}, {\"mode\": \"vega-lite\"});\n</script>",
      "text/plain": "alt.Chart(...)"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chart_perf"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/html": "\n<div id=\"altair-viz-992755ae94244d7190a19ccde51bb3d4\"></div>\n<script type=\"text/javascript\">\n  (function(spec, embedOpt){\n    let outputDiv = document.currentScript.previousElementSibling;\n    if (outputDiv.id !== \"altair-viz-992755ae94244d7190a19ccde51bb3d4\") {\n      outputDiv = document.getElementById(\"altair-viz-992755ae94244d7190a19ccde51bb3d4\");\n    }\n    const paths = {\n      \"vega\": \"https://cdn.jsdelivr.net/npm//vega@5?noext\",\n      \"vega-lib\": \"https://cdn.jsdelivr.net/npm//vega-lib?noext\",\n      \"vega-lite\": \"https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext\",\n      \"vega-embed\": \"https://cdn.jsdelivr.net/npm//vega-embed@6?noext\",\n    };\n\n    function loadScript(lib) {\n      return new Promise(function(resolve, reject) {\n        var s = document.createElement('script');\n        s.src = paths[lib];\n        s.async = true;\n        s.onload = () => resolve(paths[lib]);\n        s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n        document.getElementsByTagName(\"head\")[0].appendChild(s);\n      });\n    }\n\n    function showError(err) {\n      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n      throw err;\n    }\n\n    function displayChart(vegaEmbed) {\n      vegaEmbed(outputDiv, spec, embedOpt)\n        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n    }\n\n    if(typeof define === \"function\" && define.amd) {\n      requirejs.config({paths});\n      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n    } else if (typeof vegaEmbed === \"function\") {\n      displayChart(vegaEmbed);\n    } else {\n      loadScript(\"vega\")\n        .then(() => loadScript(\"vega-lite\"))\n        .then(() => loadScript(\"vega-embed\"))\n        .catch(showError)\n        .then(() => displayChart(vegaEmbed));\n    }\n  })({\"config\": {\"view\": {\"continuousWidth\": 400, \"continuousHeight\": 300}, \"point\": {\"size\": 50}}, \"data\": {\"name\": \"data-845eaefd7b025d959b0bf303f8f6292d\"}, \"mark\": {\"type\": \"line\", \"interpolate\": \"monotone\", \"point\": true}, \"encoding\": {\"color\": {\"type\": \"nominal\", \"field\": \"category\", \"legend\": {\"orient\": \"top-left\", \"title\": null}, \"scale\": {\"scheme\": \"dark2\"}}, \"x\": {\"type\": \"ordinal\", \"axis\": {\"tickCount\": 8}, \"field\": \"Nodes\", \"scale\": {\"zero\": false}}, \"y\": {\"type\": \"quantitative\", \"field\": \"Time\", \"scale\": {\"type\": \"log\"}, \"title\": \"Time (s)\"}}, \"width\": 400, \"$schema\": \"https://vega.github.io/schema/vega-lite/v4.8.1.json\", \"datasets\": {\"data-845eaefd7b025d959b0bf303f8f6292d\": [{\"Nodes\": 4.0, \"category\": \"GNN Time\", \"Time\": 0.00022852365539874882}, {\"Nodes\": 8.0, \"category\": \"GNN Time\", \"Time\": 0.0002507899936987087}, {\"Nodes\": 12.0, \"category\": \"GNN Time\", \"Time\": 0.0002826356024015695}, {\"Nodes\": 16.0, \"category\": \"GNN Time\", \"Time\": 0.0003434713051887229}, {\"Nodes\": 20.0, \"category\": \"GNN Time\", \"Time\": 0.0004007225688081235}, {\"Nodes\": 24.0, \"category\": \"GNN Time\", \"Time\": 0.0004910203024977818}, {\"Nodes\": 28.0, \"category\": \"GNN Time\", \"Time\": 0.0005519005811074749}, {\"Nodes\": 32.0, \"category\": \"GNN Time\", \"Time\": 0.0007097476718947291}, {\"Nodes\": 4.0, \"category\": \"Heuristic Time\", \"Time\": 0.0001130219531012699}, {\"Nodes\": 8.0, \"category\": \"Heuristic Time\", \"Time\": 0.0005498815431026742}, {\"Nodes\": 12.0, \"category\": \"Heuristic Time\", \"Time\": 0.0014672649493906646}, {\"Nodes\": 16.0, \"category\": \"Heuristic Time\", \"Time\": 0.0033623406334081663}, {\"Nodes\": 20.0, \"category\": \"Heuristic Time\", \"Time\": 0.0067811725919134916}, {\"Nodes\": 24.0, \"category\": \"Heuristic Time\", \"Time\": 0.012288867411599494}, {\"Nodes\": 28.0, \"category\": \"Heuristic Time\", \"Time\": 0.02232005330340471}, {\"Nodes\": 32.0, \"category\": \"Heuristic Time\", \"Time\": 0.03717202813008334}, {\"Nodes\": 4.0, \"category\": \"Exhaustive Time\", \"Time\": 3.0225994600914418e-05}, {\"Nodes\": 8.0, \"category\": \"Exhaustive Time\", \"Time\": 0.0002816980701871216}, {\"Nodes\": 12.0, \"category\": \"Exhaustive Time\", \"Time\": 0.0019309956108918413}, {\"Nodes\": 16.0, \"category\": \"Exhaustive Time\", \"Time\": 0.012367009829496964}, {\"Nodes\": 20.0, \"category\": \"Exhaustive Time\", \"Time\": 0.07094453831671271}, {\"Nodes\": 24.0, \"category\": \"Exhaustive Time\", \"Time\": 0.396781425341405}, {\"Nodes\": 28.0, \"category\": \"Exhaustive Time\", \"Time\": 2.130370435597212}, {\"Nodes\": 32.0, \"category\": \"Exhaustive Time\", \"Time\": 11.687468011836103}, {\"Nodes\": 4.0, \"category\": \"Max Power Time\", \"Time\": 2.049776283092797e-06}, {\"Nodes\": 8.0, \"category\": \"Max Power Time\", \"Time\": 2.567953919060528e-06}, {\"Nodes\": 12.0, \"category\": \"Max Power Time\", \"Time\": 2.639396395534277e-06}, {\"Nodes\": 16.0, \"category\": \"Max Power Time\", \"Time\": 2.7560215909034014e-06}, {\"Nodes\": 20.0, \"category\": \"Max Power Time\", \"Time\": 3.123552491888404e-06}, {\"Nodes\": 24.0, \"category\": \"Max Power Time\", \"Time\": 3.5849320935085417e-06}, {\"Nodes\": 28.0, \"category\": \"Max Power Time\", \"Time\": 3.670072602108121e-06}, {\"Nodes\": 32.0, \"category\": \"Max Power Time\", \"Time\": 3.6168976919725537e-06}, {\"Nodes\": 4.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 5.965040111914277e-06}, {\"Nodes\": 8.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 1.578141781501472e-05}, {\"Nodes\": 12.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 3.15261143958196e-05}, {\"Nodes\": 16.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 5.158597240224481e-05}, {\"Nodes\": 20.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 7.439401189330965e-05}, {\"Nodes\": 24.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 0.00010746516410727054}, {\"Nodes\": 28.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 0.0001416386622004211}, {\"Nodes\": 32.0, \"category\": \"WMMSE with Max Power Time\", \"Time\": 0.0001949552500853315}]}}, {\"mode\": \"vega-lite\"});\n</script>",
      "text/plain": "alt.Chart(...)"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chart_time"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Plot in SVG format for viewing on Github"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "<img src=\"https://user-images.githubusercontent.com/17931435/213001877-d6b2fd74-dd3b-4987-b421-9ae9cdbd3a38.svg\" width=\"450\">\n",
    "<img src=\"https://user-images.githubusercontent.com/17931435/213001470-8ef72cdc-4b39-4af6-9325-4ed355dbb843.svg\" width=\"450\">"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}