discrete/Minimum cost bipartite matching.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ebc7dc1e",
   "metadata": {},
   "source": [
    "## Monge formulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f35c638",
   "metadata": {},
   "source": [
    "Let $(\\Omega_{X}, F_{X}, \\mu)$ and $(\\Omega_{Y}, F_{Y}, \\nu)$ be two probability spaces with $\\mu$ and $\\nu$ discrete measures.\n",
    "The Monge formulation of the optimal transport problem is \n",
    "\n",
    "<font color=\"blue\">\n",
    "$$\\min \\left\\{ \\sum_{X} c_{T}(x) \\mu(x) : T_{\\#}(\\mu) = \\nu \\right\\}$$\n",
    "</font>\n",
    "\n",
    "where $T_{\\#}$ is the pushforward measure of $\\mu$ by $T$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcfc603b",
   "metadata": {},
   "source": [
    "If $X: \\Omega_{X} \\rightarrow \\mathbb{R}$ and $Y: \\Omega_{Y} \\rightarrow \\mathbb{R}$ are two discrete random variables with $\\Omega_{X} = \\Omega_{Y} = [1, \\ldots, N]$, this formulation is equivalent to\n",
    "\n",
    "<font color=\"blue\">\n",
    "$$ \\begin{array}{c}\\text{min}\\\\ \\sigma \\in \\Pi_{N}\\end{array}\n",
    "\\left\\{ \\sum_{i=1}^{N} C_{i},\\sigma(i) \\right\\}$$\n",
    "</font>\n",
    "\n",
    "where $\\Pi_{N}$ is the set of all the permutation matrices of $\\{1, \\ldots, N\\} \\text{x} \\{1, \\ldots, N\\}$, $\\sigma \\in \\Pi_{N}$ a permutation matrix and $\\sigma(i)$ the ith row of $\\sigma$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d86b0aba-e731-436c-bc7a-108e78220da8",
   "metadata": {},
   "source": [
    "### Importing libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "98d63896",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "plt.style.use(\"science\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0971529a",
   "metadata": {},
   "source": [
    "### Bakeries and cafeterias"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a4d0107",
   "metadata": {},
   "source": [
    "Suppose we have N bakeries and N cafeterias. A bakery can deliver to only one cafeteria. The cost of the ith bakery supplying the jth cafeteria is given by the following matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f2fef142",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 6\n",
    "C = np.array([[12., 10., 31., 27., 10., 30.],\n",
    "              [22.,  7., 25., 15., 11., 14.],\n",
    "              [19.,  7., 19., 10., 15., 15.],\n",
    "              [10.,  6., 21., 19., 14., 24.],\n",
    "              [15., 23., 14., 24., 31., 34.],\n",
    "              [35., 26., 16.,  9., 34., 15.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e8f09276",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 6)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51510018",
   "metadata": {},
   "source": [
    "We want to minimize the total cost of supplying all the N cafeterias.\n",
    "This is a problem of finding an optimal transport map i.e. an application T that maps a bakery to a cafeteria \n",
    "and minimizes the total cost."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e89f78",
   "metadata": {},
   "source": [
    "The number of possibilities is\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\left( \\begin{array}{cc}6\\\\1\\end{array} \\right) * \\left( \\begin{array}{cc}5\\\\1\\end{array} \\right) * ... * \\left( \\begin{array}{cc}2\\\\1\\end{array} \\right) * 1 = 6!\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eb7a7db3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "720"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.factorial(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d29201cd",
   "metadata": {},
   "source": [
    "One of these 720 possibilities is for the ith bakery to supply the ith cafeteria. The permutation matrix is $\\sigma = I_{N}$ the identity matrix. The cost is the sum of the diagonal "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "682dbf24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(C).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6405193",
   "metadata": {},
   "source": [
    "Instead of testing all the N! possible solutions which is impractical, we formulate the problem as follow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d818cc25",
   "metadata": {},
   "source": [
    "$$\\begin{array}{c}\\text{min}\\\\ \\sigma \\in \\Pi_{N}\\end{array} \\left\\{ \\sum_{i=1}^{N} C_{i},\\sigma(i) \\right\\}$$\n",
    "\n",
    "where $C$ is the cost and $\\sigma$ is a permutation matrix of $\\{1, \\ldots, N\\} \\text{x} \\{1, \\ldots, N\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6862f73c",
   "metadata": {},
   "source": [
    "### Optimal transport as minimum cost bipartite matching"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eed790d",
   "metadata": {},
   "source": [
    "Let's construct a graph where both the bakeries and the cafeterias are the nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "03647467",
   "metadata": {},
   "outputs": [],
   "source": [
    "g = nx.Graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a7e0e0d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nodes x : x0 x1 x2 x3 x4 x5\n",
      "Nodes y : y0 y1 y2 y3 y4 y5\n"
     ]
    }
   ],
   "source": [
    "nodes_x = ['x' + str(_x) for _x in list(range(N))]\n",
    "nodes_y = ['y' + str(_y) for _y in list(range(N))]\n",
    "print(\"Nodes x :\", *nodes_x)\n",
    "print(\"Nodes y :\", *nodes_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "811c3dd1",
   "metadata": {},
   "source": [
    "**Adding the nodes to the graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "185e7437",
   "metadata": {},
   "outputs": [],
   "source": [
    "for node in nodes_x + nodes_y:\n",
    "    g.add_node(node)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5319fecf",
   "metadata": {},
   "source": [
    "**Adding the edges**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4b6a39f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        g.add_edge(nodes_x[i], nodes_y[j], weight=C[i, j])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "007b1d28",
   "metadata": {},
   "source": [
    "**Drawing the bipartite graph**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e054cf1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_graph(g, filename = \"\", layout = \"bipartite\"):\n",
    "    fig = plt.figure(figsize=(5, 2))\n",
    "    if layout == \"bipartite\" :\n",
    "        pos = nx.bipartite_layout(g, nodes_x, align = 'horizontal')\n",
    "    else:\n",
    "        pos = nx.spring_layout(g, nodes_x)\n",
    "    nx.draw_networkx_nodes(g, pos, nodelist=nodes_x, node_color = 'silver', node_size = 400)\n",
    "    nx.draw_networkx_nodes(g, pos, nodelist=nodes_y, node_color = 'skyblue', node_size = 400)\n",
    "    nx.draw_networkx_labels(g, pos, font_color = 'black')\n",
    "    nx.draw_networkx_edges(g, pos)\n",
    "    edge_labels = nx.get_edge_attributes(g, 'weight')\n",
    "    nx.draw_networkx_edge_labels(g, pos, edge_labels)\n",
    "    plt.axis('off')\n",
    "    plt.tight_layout()\n",
    "    if filename != \"\":\n",
    "        plt.savefig(filename)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e72cd4fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_graph(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e842233c",
   "metadata": {},
   "source": [
    "This is a bipartite graph, its vertices are divided into two disjoint sets $X = \\{ x_{0}, x_{1}, ..., x_{5} \\}$ and\n",
    "$Y = \\{ y_{0}, y_{1}, ..., y_{5}\\}$\n",
    "\n",
    "The optimal transport problem formulated above is the problem finding a matching in a bipartite graph for which the sum of the weight of the edges is minimum."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41d96ac3",
   "metadata": {},
   "source": [
    "**Solving the problem**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a363697d",
   "metadata": {},
   "source": [
    "Many polynomial time (in the number of vertices $N$) algorithms for solving this problem exists.\n",
    "The Hopcroft-karp algotihm is implemented in scipy and can be called from networkx to find the minimum bipartite matching of a graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1a398b1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'x1': 'y5',\n",
       " 'x2': 'y1',\n",
       " 'x5': 'y3',\n",
       " 'x4': 'y2',\n",
       " 'x3': 'y0',\n",
       " 'x0': 'y4',\n",
       " 'y5': 'x1',\n",
       " 'y1': 'x2',\n",
       " 'y3': 'x5',\n",
       " 'y2': 'x4',\n",
       " 'y0': 'x3',\n",
       " 'y4': 'x0'}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = nx.bipartite.minimum_weight_full_matching(g)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bddad4c",
   "metadata": {},
   "source": [
    "The minimum cost is the sum of the weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cfda451e",
   "metadata": {},
   "outputs": [],
   "source": [
    "min_cost = 0.\n",
    "for src, dest in res.items():\n",
    "    min_cost += g.get_edge_data(src, dest)['weight']\n",
    "min_cost /= 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ade52659",
   "metadata": {},
   "source": [
    "The minimum cost is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "446adbce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d243bdd5",
   "metadata": {},
   "source": [
    "**Visual checking**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1e4335e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (4, 4))\n",
    "ax.matshow(C, cmap = mpl.colors.ListedColormap([\"white\"]))\n",
    "ax.set_title(\"Optimal transport plan\")\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        nodex = nodes_x[i]\n",
    "        nodey = nodes_y[j]\n",
    "        if (res[nodex] == nodey):\n",
    "            color = 'red'\n",
    "        else:\n",
    "            color = 'black'\n",
    "        ax.text(j, i, int(C[i, j]), horizontalalignment = 'center',\n",
    "                verticalalignment = 'center', weight = 'bold', color = color)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a3ea11",
   "metadata": {},
   "source": [
    "If we sum the values in white we have indeed the minimum cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "baf54d1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10 + 7 + 14 + 9 + 10 + 14"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "967a20f1",
   "metadata": {},
   "source": [
    "The solution is for the bakery 3 to supply the cafeteria 0, the bakery 2 to supply the cafeteria 1, \n",
    "the bakery 4 to supply the cafeteria 2 and so on..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e8dff72",
   "metadata": {},
   "source": [
    "The optimal transport matrix is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "eabecc18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 1.],\n",
       "       [0., 1., 0., 0., 0., 0.],\n",
       "       [1., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.zeros((N, N))\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        x = nodes_x[i]\n",
    "        y = nodes_y[j]\n",
    "        z[i,j] = (res[x] == y)\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d9f55ac",
   "metadata": {},
   "source": [
    "z is the permutation matrix that minimizes the transportation cost\n",
    "\n",
    "$$z = \\begin{array}{c}\\text{argmin}\\\\ \\sigma \\in \\Pi_{N}\\end{array} \\sum_{i=1}^{N} C_{i},\\sigma(i)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9980a9fe-beec-4578-af62-47e1e55def3d",
   "metadata": {},
   "source": [
    "The corresponding bipartite graph is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a6e5cf70",
   "metadata": {},
   "outputs": [],
   "source": [
    "sg = nx.Graph()\n",
    "nodes_x = ['x' + str(_x) for _x in list(range(N))]\n",
    "nodes_y = ['y' + str(_y) for _y in list(range(N))]\n",
    "for node in nodes_x + nodes_y:\n",
    "    sg.add_node(node)\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        nodex = nodes_x[i]\n",
    "        nodey = nodes_y[j]\n",
    "        if (res[nodex] == nodey):\n",
    "            sg.add_edge(nodex, nodey, weight=C[i, j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "37056e96-d249-45a7-bfd8-09311dedd5d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#draw_graph(sg, layout = \"planar\")\n",
    "fig = plt.figure(figsize=(5, 2))\n",
    "# Layout\n",
    "pos = nx.spring_layout(sg, k = 4, seed = 10)\n",
    "# Nodes\n",
    "nx.draw_networkx_nodes(sg, pos, nodelist=nodes_x, node_color = 'silver', node_size = 400)\n",
    "nx.draw_networkx_nodes(sg, pos, nodelist=nodes_y, node_color = 'skyblue', node_size = 400)\n",
    "# Nodes labels\n",
    "nx.draw_networkx_labels(sg, pos, font_color = 'black')\n",
    "# Edges\n",
    "nx.draw_networkx_edges(sg, pos, style = \"dashed\")\n",
    "# Edge weights labels\n",
    "edge_labels = nx.get_edge_attributes(sg, 'weight')\n",
    "nx.draw_networkx_edge_labels(sg, pos, edge_labels, font_color = 'black')\n",
    "plt.axis('off')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "473c8cba-951e-48e4-9718-7fef9b42ac65",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "256f61f3-2a84-45b7-8c9d-03e4b33a51e6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}