CSP/CSP_graph_coloring_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constraint Satisfaction Problem : Graph coloring\n",
    "\n",
    "\n",
    "## Create Data\n",
    "\n",
    "We can create a planar graph with $n$ vertices by randomly placing $n$ points in 2-dimensional Euclidean space and then performing a [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial import Delaunay\n",
    "\n",
    "np.random.seed(1111)\n",
    "\n",
    "# create points and sort them by \n",
    "n = 10\n",
    "points = np.random.randint(100, size=(n, 2))\n",
    "o = np.argsort(points[:,0])\n",
    "points = points[o,:]\n",
    "\n",
    "\n",
    "# triangulate\n",
    "tri = Delaunay(points)\n",
    "\n",
    "\n",
    "# plot\n",
    "plt.triplot(points[:,0], points[:,1], tri.simplices, color = \"gray\")\n",
    "plt.plot(points[:,0], points[:,1], 'o', color = \"green\", markersize = 20)\n",
    "\n",
    "for i in range(len(points)):\n",
    "       plt.annotate(i, points[i,:], \n",
    "        color='white', fontsize=\"large\", weight='heavy',\n",
    "        horizontalalignment='center', verticalalignment='center')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The triangulation can be converted into a list with an array of neighbor vertex indices for each point (see man page for [scipy.spatial.Delaunay](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Delaunay.html)). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([1, 2, 4, 5], dtype=int32),\n",
       " array([0, 5, 7], dtype=int32),\n",
       " array([0, 3, 4, 9], dtype=int32),\n",
       " array([2, 4, 9], dtype=int32),\n",
       " array([0, 2, 3, 5, 6, 8, 9], dtype=int32),\n",
       " array([0, 1, 4, 6, 7], dtype=int32),\n",
       " array([4, 5, 7, 8], dtype=int32),\n",
       " array([1, 5, 6, 8], dtype=int32),\n",
       " array([4, 6, 7, 9], dtype=int32),\n",
       " array([2, 3, 4, 8], dtype=int32)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(indptr, indices) = tri.vertex_neighbor_vertices\n",
    "\n",
    "neighbors = []\n",
    "\n",
    "for k in range(len(indptr)-1):\n",
    "    neighbors.append(np.sort(indices[indptr[k]:indptr[k+1]]))\n",
    "    \n",
    "neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first row are the indices for the points neighboring point 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define CSP\n",
    "\n",
    "The problem is defined as a dictionary with variable names, a dictionary with domain values for each variable and a set of binary  not-equal constraints (tuples of variables that are not allowed to have the same value).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'variables': ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'],\n",
       " 'domains': {'0': ['red', 'blue', 'green', 'orange'],\n",
       "  '1': ['red', 'blue', 'green', 'orange'],\n",
       "  '2': ['red', 'blue', 'green', 'orange'],\n",
       "  '3': ['red', 'blue', 'green', 'orange'],\n",
       "  '4': ['red', 'blue', 'green', 'orange'],\n",
       "  '5': ['red', 'blue', 'green', 'orange'],\n",
       "  '6': ['red', 'blue', 'green', 'orange'],\n",
       "  '7': ['red', 'blue', 'green', 'orange'],\n",
       "  '8': ['red', 'blue', 'green', 'orange'],\n",
       "  '9': ['red', 'blue', 'green', 'orange']},\n",
       " 'constraints': dict_keys([('0', '1'), ('0', '2'), ('0', '4'), ('0', '5'), ('1', '5'), ('1', '7'), ('2', '3'), ('2', '4'), ('2', '9'), ('3', '4'), ('3', '9'), ('4', '5'), ('4', '6'), ('4', '8'), ('4', '9'), ('5', '6'), ('5', '7'), ('6', '7'), ('6', '8'), ('7', '8'), ('8', '9')])}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variables = [str(var) for var in range(n)]\n",
    "\n",
    "domain = ['red', 'blue', 'green', 'orange']\n",
    "#domain = ['red', 'blue', 'green']\n",
    "domains = {}\n",
    "for v in variables: \n",
    "    domains[v] = domain\n",
    "\n",
    "# create binary constraints\n",
    "constraints = {}\n",
    "for i in range(len(neighbors)):\n",
    "    for j in neighbors[i]:\n",
    "        if(i<j): constraints[tuple([str(i), str(j)])] = True\n",
    "constraints = constraints.keys()\n",
    "\n",
    "csp = {'variables': variables, 'domains': domains, 'constraints': constraints, }\n",
    "csp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check Completeness and Consistency\n",
    "\n",
    "`assignment` is a dictionary. Assigned variables have an entry with the variable name as the key. `{}` is therefore the empty assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "complete({}, csp) = False\n",
      "complete({...complete list...}, csp) = True\n"
     ]
    }
   ],
   "source": [
    "def complete(assignment, csp):\n",
    "    return(all([v in assignment.keys() for v in csp['variables']])) \n",
    "\n",
    "print(\"complete({}, csp) =\", complete({}, csp))\n",
    "\n",
    "print(\"complete({...complete list...}, csp) =\", \n",
    "      complete({'0': 'red', '1': 'red', '2': 'red', '3': 'red', '4': 'red', \n",
    "          '5': 'red', '6': 'red', '7': 'red', '8': 'red', '9': 'red'}, csp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "consistent({}, csp) = True\n",
      "consistent({'0': 'red', '1': 'red', '2': 'blue'}, csp) = False\n"
     ]
    }
   ],
   "source": [
    "def consistent(assignment, csp):\n",
    "    for constr in csp['constraints']:\n",
    "        if(constr[0] in assignment.keys() and constr[1] in assignment.keys()):\n",
    "            if assignment[constr[0]] == assignment[constr[1]]: return(False)\n",
    "        \n",
    "    return(True)\n",
    "        \n",
    "print(\"consistent({}, csp) =\", consistent({}, csp))\n",
    "print(\"consistent({'0': 'red', '1': 'red', '2': 'blue'}, csp) =\", \n",
    "      consistent({'0': 'red', '1': 'red', '2': 'blue'}, csp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implement Simple Backtracking Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "select_unassigned_var({'0': 'red', '1': 'blue'}, csp) = 2\n"
     ]
    }
   ],
   "source": [
    "# TODO: implement variable ordering. Choose variable with the minimum-remaining-values (MRV)\n",
    "def select_unassigned_var(assignment, csp):\n",
    "    if(complete(assignment, csp)): return(None)\n",
    "    \n",
    "    return(csp['variables'][np.where([not v in assignment.keys() for v in csp['variables']])[0][0]])\n",
    "\n",
    "print(\"select_unassigned_var({'0': 'red', '1': 'blue'}, csp) =\", \n",
    "     select_unassigned_var({'0': 'red', '1': 'blue'}, csp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# I use a global variable to turn on verbose mode in the recursion\n",
    "#VERBOSE = True\n",
    "VERBOSE = False\n",
    "COUNT = 0\n",
    "\n",
    "# returns None for failure\n",
    "def backtrack_search(csp):\n",
    "    global COUNT\n",
    "    COUNT = 0\n",
    "    \n",
    "    assignment = backtrack({}, csp)\n",
    "    \n",
    "    print(f\"Checked nodes: {COUNT}\")\n",
    "    \n",
    "    return assignment\n",
    "\n",
    "def backtrack(assignment, csp):\n",
    "    global VERBOSE, COUNT\n",
    "    \n",
    "    COUNT += 1\n",
    "    \n",
    "    if complete(assignment, csp): \n",
    "        return assignment\n",
    "    \n",
    "    var = select_unassigned_var(assignment, csp)\n",
    "    \n",
    "    # TODO: implement value ordering. Use the least-constraining-vaue heuristic. \n",
    "    # for val in order_domain(assignment, var, csp)\n",
    "    for val in csp['domains'][var]:\n",
    "        assignment[var] = val\n",
    "        \n",
    "        if VERBOSE: print(f\"Checking: {assignment}\")\n",
    "        \n",
    "        if consistent(assignment, csp):\n",
    "            \n",
    "            #TODO: add inference for early failing (forward checking, )\n",
    "            # if inference_fails(assignment, csp): return(None)\n",
    "            result = backtrack(assignment, csp)\n",
    "            if not result is None:\n",
    "                    return(result)\n",
    "                \n",
    "        del assignment[var]\n",
    "        \n",
    "    if verbose: print(f\"Backtracking\")\n",
    "    return(None) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run Backtracking Search on the Random Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checked nodes: 11\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'0': 'red',\n",
       " '1': 'blue',\n",
       " '2': 'blue',\n",
       " '3': 'red',\n",
       " '4': 'green',\n",
       " '5': 'orange',\n",
       " '6': 'red',\n",
       " '7': 'green',\n",
       " '8': 'blue',\n",
       " '9': 'orange'}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.27 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1 display(backtrack_search(csp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the resulting coloring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.triplot(points[:,0], points[:,1], tri.simplices, color = \"gray\")\n",
    "\n",
    "for i in range(len(points)):\n",
    "        plt.plot(points[i:,0], points[i:,1], 'o', color = list(res.values())[i], markersize = 20)\n",
    "        plt.annotate(i, points[i,:], \n",
    "        color='white', fontsize=\"large\", weight='heavy',\n",
    "        horizontalalignment='center', verticalalignment='center')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assignment\n",
    "\n",
    "Implement the following graph coloring algorithms:\n",
    "\n",
    "* Add variable and value ordering to the implementation.\n",
    "* Add forward checking to the implementation.\n",
    "* Implement hill climbing local search with the min-conflicts heuristic.\n",
    "\n",
    "Try to color graphs of several sizes with 3 and 4 colors. For each $n$, generate several random instances, and try to make n as large as you can manage. On average, how many constraints (edges) do your map coloring instances have for each $n$? Report the performance of each search algorithm as a function of $n$. For both variants of backtracking search, you can characterize performance in terms of the number of variable assignments attempted. For hill climbing search, report the number of uphill moves and random restarts required in order to reach a solution. Of course, you can also report raw running times as a function of $n$."
   ]
  }
 ],
 "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}