ND_Homework1.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Netwok Dynamics\n",
        "## Homework 1"
      ],
      "metadata": {
        "id": "bYTWCqenWF6U"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Exercise 1"
      ],
      "metadata": {
        "id": "mR6JnWtn1CWA"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "8-W8RU_HSlJQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "outputId": "fbd0d689-e829-4ae3-8e0c-688acd72b5c1"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_edges_from([\n",
        "    ('o', 'a'),\n",
        "    ('o', 'b'),\n",
        "    ('a', 'd'),\n",
        "    ('b', 'd'),\n",
        "    ('b', 'c'),\n",
        "    ('c', 'd')\n",
        "])\n",
        "\n",
        "pos = {\n",
        "    'o': (40, 20),\n",
        "    'a': (60, 35),\n",
        "    'c': (60, 5),\n",
        "    'd': (80, 20),\n",
        "    'b': (60, 20)\n",
        "}\n",
        "\n",
        "edge_labels = {\n",
        "    ('o', 'a'): 'e1',\n",
        "    ('o', 'b'): 'e3',\n",
        "    ('a', 'd'): 'e2',\n",
        "    ('b', 'd'): 'e4',\n",
        "    ('b', 'c'): 'e5',\n",
        "    ('c', 'd'): 'e6'\n",
        "}\n",
        "\n",
        "G['o']['a']['capacity'] = 3\n",
        "G['o']['b']['capacity'] = 3\n",
        "G['a']['d']['capacity'] = 2\n",
        "G['b']['d']['capacity'] = 2\n",
        "G['b']['c']['capacity'] = 3\n",
        "G['c']['d']['capacity'] = 1\n",
        "\n",
        "nx.draw(G, pos, with_labels=True, font_color=\"white\", node_size=800)\n",
        "nx.draw_networkx_edge_labels(G, pos, font_color='black', edge_labels=edge_labels)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point a\n",
        "(tau, min_cut) = nx.algorithms.flow.minimum_cut(G, 'o', 'd')\n",
        "print(f\"tau: {tau}, min cut: {min_cut}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vP3ehoMkad0W",
        "outputId": "5ada2eb3-d9cc-4788-f863-a862b9cb5555"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tau: 5, min cut: ({'c', 'a', 'b', 'o'}, {'d'})\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point b\n",
        "\n",
        "\n",
        "print(\"Maximum flow: \", nx.algorithms.flow.maximum_flow(G, 'o', 'd'))\n",
        "\n",
        "# We used the previous result function to generate such labels\n",
        "edge_labels = {\n",
        "    ('o', 'a'): '2/3',\n",
        "    ('o', 'b'): '3/3',\n",
        "    ('a', 'd'): '2/2',\n",
        "    ('b', 'd'): '2/2',\n",
        "    ('b', 'c'): '1/3',\n",
        "    ('c', 'd'): '1/1'\n",
        "}\n",
        "\n",
        "plt.subplot(211)\n",
        "nx.draw(G, pos, with_labels=True, font_color=\"white\")\n",
        "nx.draw_networkx_edge_labels(G, pos, font_color='black', edge_labels=edge_labels)\n",
        "\n",
        "edge_labels = {('o', 'a'): '1/3', ('b', 'c'): '2/3'}\n",
        "\n",
        "plt.subplot(212)\n",
        "nx.draw(G, pos, with_labels=True, font_color=\"white\")\n",
        "nx.draw_networkx_edge_labels( G, pos, font_color='black', edge_labels=edge_labels)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "8Z907t_IbQoo",
        "outputId": "581f2111-0d06-4549-f33b-b38a742f4acc"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Maximum flow:  (5, {'o': {'a': 2, 'b': 3}, 'a': {'d': 2}, 'b': {'d': 2, 'c': 1}, 'd': {}, 'c': {'d': 1}})\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# punto c\n",
        "\n",
        "G = nx.DiGraph()\n",
        "\n",
        "G.add_edges_from([\n",
        "    ('o', 'a'),\n",
        "    ('o', 'b'),\n",
        "    ('a', 'd'),\n",
        "    ('b', 'd'),\n",
        "    ('b', 'c'),\n",
        "    ('c', 'd')\n",
        "])\n",
        "\n",
        "G['o']['a']['capacity'] = 3\n",
        "G['o']['b']['capacity'] = 3\n",
        "G['a']['d']['capacity'] = 2\n",
        "G['b']['d']['capacity'] = 2\n",
        "G['b']['c']['capacity'] = 3\n",
        "G['c']['d']['capacity'] = 1\n",
        "\n",
        "x = range(1, 51)\n",
        "taus = []\n",
        "(tau, min_cut) = nx.algorithms.flow.minimum_cut(G, 'o', 'd')\n",
        "\n",
        "for i in x:\n",
        "    u = min_cut[0]\n",
        "    uc = min_cut[1]\n",
        "    min_capacity_ln = dict()\n",
        "    for n1 in u:\n",
        "        for n2 in uc:\n",
        "            if n2 in G.successors(n1):\n",
        "                min_capacity_ln[(n1, n2)] = G[n1][n2]['capacity']\n",
        "    min_edge = list(min_capacity_ln.keys())[0]\n",
        "    max_tau = tau\n",
        "    for key in min_capacity_ln.keys():\n",
        "      G[key[0]][key[1]]['capacity']+=1\n",
        "      (tau, min_cut) = nx.algorithms.flow.minimum_cut(G, 'o', 'd')\n",
        "      if tau >= max_tau:\n",
        "        min_edge = (key[0],key[1])\n",
        "        max_tau = tau\n",
        "      G[key[0]][key[1]]['capacity']-=1\n",
        "    G[min_edge[0]][min_edge[1]]['capacity'] += 1\n",
        "    (tau, min_cut) = nx.algorithms.flow.minimum_cut(G, 'o', 'd')\n",
        "    taus.append(tau)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(x, taus, 'r')\n",
        "ax.set_xlabel(r'$x$')\n",
        "ax.set_ylabel(r'$\\tau^{*}$')\n",
        "ax.grid(True)\n",
        "\n",
        "plt.show()\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "KkzaYW8oicYM",
        "outputId": "d1d70195-ac3a-4b64-8b73-3cf34763a286"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Exercise 2"
      ],
      "metadata": {
        "id": "yhaFZFLTzojV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "\n",
        "G.add_edges_from([\n",
        "    ('p1', 'b1'),\n",
        "    ('p1', 'b2'),\n",
        "    ('p2', 'b2'),\n",
        "    ('p2', 'b3'),\n",
        "    ('p3', 'b1'),\n",
        "    ('p3', 'b4'),\n",
        "    ('p4', 'b1'),\n",
        "    ('p4', 'b2'),\n",
        "    ('p4', 'b4')\n",
        "])\n",
        "\n",
        "pos = {\n",
        "    'p1': (40, 10),\n",
        "    'p2': (40, 20),\n",
        "    'p3': (40, 30),\n",
        "    'p4': (40, 40),\n",
        "    'b1': (60, 10),\n",
        "    'b2': (60, 20),\n",
        "    'b3': (60, 30),\n",
        "    'b4': (60, 40)\n",
        "}\n",
        "\n",
        "nx.draw(G, pos, with_labels=True, font_color=\"white\", node_size=800)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "xfAdSjmr0uTz",
        "outputId": "5bf2967a-02cd-46a1-f4ab-cca98ff24f0b"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point a\n",
        "\n",
        "G2 = G.to_directed()\n",
        "G2.add_edges_from([\n",
        "    ('o', 'p1'),\n",
        "    ('o', 'p2'),\n",
        "    ('o', 'p3'),\n",
        "    ('o', 'p4'),\n",
        "    ('b1', 'd'),\n",
        "    ('b2', 'd'),\n",
        "    ('b3', 'd'),\n",
        "    ('b4', 'd')\n",
        "])\n",
        "\n",
        "G2.remove_edges_from([\n",
        "    ('b1', 'p1'),\n",
        "    ('b2', 'p2'),\n",
        "    ('b2', 'p1'),\n",
        "    ('b2', 'p2'),\n",
        "    ('b3', 'p2'),\n",
        "    ('b1', 'p3'),\n",
        "    ('b4', 'p3'),\n",
        "    ('b1', 'p4'),\n",
        "    ('b2', 'p4'),\n",
        "    ('b4', 'p4')\n",
        "])\n",
        "\n",
        "pos2 = {\n",
        "    'p1': (40, 10),\n",
        "    'p2': (40, 20),\n",
        "    'p3': (40, 30),\n",
        "    'p4': (40, 40),\n",
        "    'b1': (60, 10),\n",
        "    'b2': (60, 20),\n",
        "    'b3': (60, 30),\n",
        "    'b4': (60, 40),\n",
        "    'o': (30, 25),\n",
        "    'd': (70, 25)\n",
        "}\n",
        "\n",
        "G2['o']['p1']['capacity'] = 1\n",
        "G2['o']['p2']['capacity'] = 1\n",
        "G2['o']['p3']['capacity'] = 1\n",
        "G2['o']['p4']['capacity'] = 1\n",
        "G2['b1']['d']['capacity'] = 1\n",
        "G2['b2']['d']['capacity'] = 1\n",
        "G2['b3']['d']['capacity'] = 1\n",
        "G2['b4']['d']['capacity'] = 1\n",
        "\n",
        "for (n1, n2, cp) in G2.edges.data('capacity'):\n",
        "    if n1 in ['p1', 'p2', 'p3', 'p4']:\n",
        "        G2[n1][n2]['capacity']=1000\n",
        "\n",
        "nx.draw(G2, pos2, with_labels=True, font_color=\"white\", node_size=800)\n",
        "\n",
        "plt.show()\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "juDalItQ4ZbZ",
        "outputId": "752f60ee-6c81-45fe-982a-87524125da2a"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(tau, min_cut) = nx.algorithms.flow.minimum_cut(G2, 'o', 'd')\n",
        "\n",
        "# Folk-Fulkerson Algorithm\n",
        "\n",
        "if tau != 4:\n",
        "    print(\"no perfect matching is present\")\n",
        "else:\n",
        "    print(\"perfect matching:\")\n",
        "    (tau, mf) = nx.algorithms.flow.maximum_flow(G2, 'o', 'd')\n",
        "    G3 = nx.Graph()\n",
        "    for n1 in mf:\n",
        "        if n1 != 'o' and n1 != 'd':\n",
        "            for adj in mf[n1]:\n",
        "                if adj != 'o' and adj != 'd' and mf[n1][adj] != 0:\n",
        "                    G3.add_edge(n1, adj)\n",
        "    nx.draw(G3, pos, with_labels=True, font_color=\"white\", node_size=800)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 534
        },
        "id": "RazlS8o8Cbvk",
        "outputId": "4a272e30-c9aa-4d76-a8b9-0f8d3d14f460"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "perfect matching:\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point b + c\n",
        "\n",
        "G2['o']['p1']['capacity']= 2\n",
        "G2['o']['p2']['capacity']= 2\n",
        "G2['o']['p3']['capacity']= 2\n",
        "G2['o']['p4']['capacity']= 3\n",
        "\n",
        "G2['b1']['d']['capacity']= 2\n",
        "G2['b2']['d']['capacity']= 3\n",
        "G2['b3']['d']['capacity']= 2\n",
        "G2['b4']['d']['capacity']= 2\n",
        "\n",
        "for (n1, n2, cp) in G2.edges.data('capacity'):\n",
        "    if n1 in ['p1', 'p2', 'p3', 'p4']:\n",
        "        G2[n1][n2]['capacity']=1\n",
        "(tau, mf)= nx.algorithms.flow.maximum_flow(G2, 'o', 'd')\n",
        "edge_labels={}\n",
        "for n1 in mf:\n",
        "  for n2 in mf[n1]:\n",
        "    edge_labels[(n1,n2)]= str(mf[n1][n2])+'/'+str(G2[n1][n2]['capacity'])\n",
        "\n",
        "nx.draw(G2, pos2, with_labels=True, font_color=\"white\", node_size=800)\n",
        "nx.draw_networkx_edge_labels( G2, pos2, font_color='black', edge_labels=edge_labels)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 828
        },
        "id": "ye7R32pao2bl",
        "outputId": "50396280-40c7-4ddd-a3ab-af7795128394"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{('p1', 'b1'): Text(50.0, 10.0, '0/1'),\n",
              " ('p1', 'b2'): Text(50.0, 15.0, '1/1'),\n",
              " ('b1', 'd'): Text(65.0, 17.5, '2/2'),\n",
              " ('b2', 'd'): Text(65.0, 22.5, '3/3'),\n",
              " ('p2', 'b2'): Text(50.0, 20.0, '1/1'),\n",
              " ('p2', 'b3'): Text(50.0, 25.0, '1/1'),\n",
              " ('b3', 'd'): Text(65.0, 27.5, '1/2'),\n",
              " ('p3', 'b1'): Text(50.0, 20.0, '1/1'),\n",
              " ('p3', 'b4'): Text(50.0, 35.0, '1/1'),\n",
              " ('b4', 'd'): Text(65.0, 32.5, '2/2'),\n",
              " ('p4', 'b1'): Text(50.0, 25.0, '1/1'),\n",
              " ('p4', 'b2'): Text(50.0, 30.0, '1/1'),\n",
              " ('p4', 'b4'): Text(50.0, 40.0, '1/1'),\n",
              " ('o', 'p1'): Text(35.0, 17.5, '1/2'),\n",
              " ('o', 'p2'): Text(35.0, 22.5, '2/2'),\n",
              " ('o', 'p3'): Text(35.0, 27.5, '2/2'),\n",
              " ('o', 'p4'): Text(35.0, 32.5, '3/3')}"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Exercise 3\n"
      ],
      "metadata": {
        "id": "a8C6YVzmwZSy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# make sure to upload the data files.\n",
        "\n",
        "import networkx as nx\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import scipy as sp\n",
        "import cvxpy as cp\n",
        "\n",
        "f = sp.io.loadmat('flow.mat')[\"flow\"].reshape(28,)\n",
        "C = sp.io.loadmat('capacities.mat')[\"capacities\"].reshape(28,)\n",
        "B = sp.io.loadmat('traffic.mat')[\"traffic\"]\n",
        "l = sp.io.loadmat('traveltime.mat')[\"traveltime\"].reshape(28,)\n",
        "\n",
        "G3 = nx.DiGraph()\n",
        "edge_labels3= {}\n",
        "\n",
        "for e in range(B.shape[1]):\n",
        "  adj=[0,0]\n",
        "  for n in range(B.shape[0]):\n",
        "    if B[n][e] == 1:\n",
        "      adj[0] = n\n",
        "    elif B[n][e] == -1:\n",
        "      adj[1] = n\n",
        "  G3.add_edge(adj[0]+1,adj[1]+1)\n",
        "  G3[adj[0]+1][adj[1]+1]['weight'] = l[e]\n",
        "  G3[adj[0]+1][adj[1]+1]['capacity'] = C[e]\n",
        "  edge_labels3[(adj[0],adj[1])] = 'e'+str(e+1)\n",
        "\n",
        "pos = {\n",
        "    1: (0, 50),\n",
        "    2: (20, 50),\n",
        "    3: (30, 50),\n",
        "    4: (50, 50),\n",
        "    5: (70, 45),\n",
        "    6: (5, 30),\n",
        "    7: (20, 30),\n",
        "    8: (30, 30),\n",
        "    9: (42.5, 35),\n",
        "    10: (20, 10),\n",
        "    11: (30, 10),\n",
        "    12: (42.5, 10),\n",
        "    13: (60, 7.5),\n",
        "    14: (70, 7.5),\n",
        "    15: (30, 0),\n",
        "    16: (47.5, -5),\n",
        "    17: (70, -7.5)\n",
        "}\n",
        "\n",
        "\n",
        "\n",
        "nx.draw(G3, pos, with_labels=True, font_color=\"white\", node_size=800)\n",
        "# TODO Change shape\n",
        "# https://networkx.org/documentation/stable/reference/drawing.html"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "4tVhgsLGwcyy",
        "outputId": "6a72e273-7872-4667-c3ac-08699a2871b3"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point a\n",
        "\n",
        "# shortest path with flow optimization in cvxpy\n",
        "\n",
        "n_edges=B.shape[1]\n",
        "n_nodes=B.shape[0]\n",
        "nu= np.zeros((n_nodes,))\n",
        "nu[0]=1\n",
        "nu[-1]=-1\n",
        "temp=np.ones((17,28))\n",
        "\n",
        "flow= cp.Variable(n_edges)\n",
        "objective= cp.Minimize(l.T @ flow)\n",
        "constraints= [ B @ flow == nu, flow>=0]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "result = prob.solve()\n",
        "sp=[]\n",
        "for i in range(len(flow.value)):\n",
        "  if flow.value[i] > 0.999:\n",
        "    sp.append('e'+str(i+1))\n",
        "print(\"nodes in the shortest path computed by CVXPY:\\n\\n\",sp)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vlRxBT82LloZ",
        "outputId": "7ca199c1-7979-4967-9488-d16fa96fc835"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "nodes in the shortest path computed by CVXPY:\n",
            "\n",
            " ['e1', 'e2', 'e9', 'e12', 'e25']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# shortest path with Networkx function (proof that the two methods return the same result)\n",
        "\n",
        "sp2= nx.shortest_path(G3,1,17,'weight')\n",
        "print(\"nodes in the shortest path computed by NetworkX:\\n\\n\",sp2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fr-jf81wSjFy",
        "outputId": "f96ce403-15fd-4db2-da2e-8bfabfec0d6f"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "nodes in the shortest path computed by NetworkX:\n",
            "\n",
            " [1, 2, 3, 9, 13, 17]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point b\n",
        "\n",
        "(tau, mf) = nx.algorithms.flow.maximum_flow(G3, 1, 17)\n",
        "print(mf)\n",
        "print('\\n\\nmaximum flow:', tau)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-VCB7f41Uo0k",
        "outputId": "2013c329-0578-44c5-ca6a-9c055e816725"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{1: {2: 8741, 6: 13707}, 2: {3: 8741, 7: 0}, 3: {4: 0, 8: 0, 9: 8741}, 4: {5: 0, 9: 0}, 5: {14: 0}, 6: {7: 4624, 10: 9083}, 7: {8: 4624, 10: 0}, 8: {9: 4624, 11: 0}, 9: {13: 6297, 12: 7068}, 13: {14: 3835, 17: 10355}, 14: {17: 3835}, 10: {11: 825, 15: 8258}, 11: {12: 825, 15: 0}, 15: {16: 8258}, 12: {13: 7893}, 17: {}, 16: {17: 8258}}\n",
            "\n",
            "\n",
            "maximum flow: 22448\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point c\n",
        "\n",
        "v = B @ f\n",
        "\n",
        "print(\"exogenous flow vector:\\n\\n\",v)\n",
        "# sanity check: all elements of v sums to 0\n",
        "sum=0\n",
        "for el in v:\n",
        "  sum+=el\n",
        "\n",
        "print(\"\\nsum of elements of v: \",sum)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8LsU9-eaXgdc",
        "outputId": "cd9a5214-3d9d-4ab2-82ae-42d4f1cba345"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "exogenous flow vector:\n",
            "\n",
            " [ 16282   9094  19448   4957   -746   4768    413     -2  -5671   1169\n",
            "     -5  -7131   -380  -7412  -7810  -3430 -23544]\n",
            "\n",
            "sum of elements of v:  0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point d\n",
        "\n",
        "flows = cp.Variable(n_edges)\n",
        "\n",
        "obj= cp.multiply(cp.multiply(C,l),cp.inv_pos(1-cp.multiply(flows,1/C)))-cp.multiply(C,l)\n",
        "\n",
        "objective = cp.Minimize(cp.sum(obj))\n",
        "nu = np.zeros((17,))\n",
        "nu[0] = 16282\n",
        "nu[-1] = -16282\n",
        "constraints = [ B @ flows == nu, flows>=0]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "result = prob.solve()\n",
        "print(\"social optimum flow:\\n\", flows.value)\n",
        "fstar = flows.value"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5E_-Gp698_xA",
        "outputId": "9c51ed0b-a97c-41ce-cd02-c67f22e24cf2"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "social optimum flow:\n",
            " [6.45413244e+03 5.91951309e+03 2.99521607e+03 2.99521399e+03\n",
            " 9.82786756e+03 4.49706077e+03 2.89732663e+03 2.43600230e+03\n",
            " 3.04736049e+03 5.34619348e+02 2.33693727e-02 2.92427365e+03\n",
            " 2.07688030e-03 2.99521399e+03 5.33080679e+03 2.73085467e+03\n",
            " 4.73430561e+03 2.13435349e+03 4.61347705e+02 2.31291754e+03\n",
            " 3.19220011e+03 5.50511764e+03 2.31057919e+03 2.26487352e-03\n",
            " 6.24189894e+03 5.30579319e+03 4.73430787e+03 4.73430787e+03]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point e\n",
        "import scipy as sp\n",
        "\n",
        "flows = cp.Variable(n_edges)\n",
        "obj=0\n",
        "for i in range(28):\n",
        "  obj += -(C[i]*l[i]*cp.log(1-(flows[i]/C[i])))\n",
        "objective = cp.Minimize(cp.sum(obj))\n",
        "nu= np.zeros((17,))\n",
        "nu[0]=16282\n",
        "nu[-1]=-16282\n",
        "constraints = [ B @ flows == nu, flows>=0]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "result = prob.solve()\n",
        "print(\"Wardrop equilibrium:\\n\",flows.value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n9gQ7VnCD-y5",
        "outputId": "4c5f9297-0f8c-4588-d986-eaefd4396d7c"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wardrop equilibrium:\n",
            " [6.53248376e+03 6.53248350e+03 2.20678748e+03 2.20678743e+03\n",
            " 9.74951620e+03 4.49336693e+03 2.71426774e+03 2.20385945e+03\n",
            " 3.34278634e+03 2.63674275e-04 1.88855724e+02 4.13684030e+03\n",
            " 4.44865186e-05 2.20678743e+03 5.25614927e+03 2.24738236e+03\n",
            " 4.78786636e+03 1.77909945e+03 6.99264014e+02 2.99791346e+03\n",
            " 2.94664631e+03 5.94455977e+03 2.50794077e+03 6.19467518e-05\n",
            " 6.77940534e+03 4.71472820e+03 4.78786643e+03 4.78786643e+03]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point f\n",
        "\n",
        "flows = cp.Variable(n_edges)\n",
        "obj=0\n",
        "for i in range(28):\n",
        "  tau= C[i]*l[i]/(C[i]-fstar[i])**2\n",
        "  w= fstar[i]* tau\n",
        "  obj += (-(C[i]*l[i]*cp.log(1-(flows[i]/C[i])))+w*flows[i])\n",
        "objective = cp.Minimize(obj)\n",
        "nu= np.zeros((17,))\n",
        "nu[0]=16282\n",
        "nu[-1]=-16282\n",
        "constraints = [ B @ flows == nu, flows>=0]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "result = prob.solve()\n",
        "print(\"Wardrop equilibrium with tolls:\\n\",flows.value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GREplkRnPZw1",
        "outputId": "97b75411-323f-48af-c942-45d4bacd7284"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wardrop equilibrium with tolls:\n",
            " [6.45403281e+03 5.91917481e+03 2.99543409e+03 2.99543402e+03\n",
            " 9.82796712e+03 4.49711434e+03 2.89764345e+03 2.43596652e+03\n",
            " 3.04726122e+03 5.34857999e+02 3.16772122e-04 2.92374040e+03\n",
            " 6.65267070e-05 2.99543402e+03 5.33085278e+03 2.73088365e+03\n",
            " 4.73429802e+03 2.13432889e+03 4.61677250e+02 2.31244576e+03\n",
            " 3.19256081e+03 5.50500657e+03 2.31046294e+03 8.60865914e-05\n",
            " 6.24180486e+03 5.30589696e+03 4.73429810e+03 4.73429810e+03]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# point g\n",
        "\n",
        "flows = cp.Variable(n_edges)\n",
        "obj= cp.multiply(cp.multiply(C,l),cp.inv_pos(1-cp.multiply(flows,1/C)))-cp.multiply(C,l)-cp.multiply(flows,l)\n",
        "objective = cp.Minimize(cp.sum(obj))\n",
        "nu= np.zeros((17,))\n",
        "nu[0]=16282\n",
        "nu[-1]=-16282\n",
        "constraints = [ B @ flows == nu, flows>=0]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "result = prob.solve()\n",
        "print(\"social optimum flow:\\n\\n\",flows.value)\n",
        "fstar= flows.value\n",
        "\n",
        "flowsW = cp.Variable(n_edges)\n",
        "obj=0\n",
        "for i in range(28):\n",
        "  w= fstar[i]* (C[i]*l[i]/(C[i]-fstar[i])**2)-l[i]\n",
        "  obj += (-(C[i]*l[i]*cp.log(1-(flowsW[i]/C[i])))+w*flowsW[i])\n",
        "objective = cp.Minimize(obj)\n",
        "constraints = [ B @ flowsW == nu, flowsW>=0]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "result = prob.solve()\n",
        "print(\"\\nWardrop equilibrium with tolls:\\n\\n\",flowsW.value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7lFqoCVGRV_x",
        "outputId": "108ceafa-3a36-42a8-ee7d-920097552223"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "social optimum flow:\n",
            "\n",
            " [6.46809217e+03 5.61773555e+03 3.29769367e+03 3.29768171e+03\n",
            " 9.81390783e+03 4.50158117e+03 3.00293310e+03 2.56427919e+03\n",
            " 2.91777669e+03 8.50356614e+02 2.08434100e-02 2.32002104e+03\n",
            " 1.19593596e-02 3.29768171e+03 5.31232667e+03 2.93160156e+03\n",
            " 4.72972979e+03 2.34900468e+03 4.38674749e+02 1.96653550e+03\n",
            " 3.37027250e+03 5.33680800e+03 2.14286457e+03 3.80367843e-03\n",
            " 6.11172012e+03 5.44054629e+03 4.72973360e+03 4.72973360e+03]\n",
            "\n",
            "Wardrop equilibrium with tolls:\n",
            "\n",
            " [6.46808645e+03 5.61859814e+03 3.29731020e+03 3.29730927e+03\n",
            " 9.81391339e+03 4.50161236e+03 3.00250902e+03 2.56379914e+03\n",
            " 2.91794392e+03 8.49488310e+02 1.50264139e-03 2.32128644e+03\n",
            " 9.28476720e-04 3.29730927e+03 5.31230103e+03 2.93120598e+03\n",
            " 4.72968670e+03 2.34859165e+03 4.38711380e+02 1.96714259e+03\n",
            " 3.36991700e+03 5.33705958e+03 2.14316481e+03 3.61410428e-04\n",
            " 6.11183869e+03 5.44047409e+03 4.72968707e+03 4.72968707e+03]\n"
          ]
        }
      ]
    }
  ]
}