doc/OpenAnalysis/07 - Dynamic Programming Based Graph Algorithms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic Programming  based  Graph Algorithms\n",
    "\n",
    "These class of algorithms takes a Graph as input, using it's adjacancy matrix , generates result matrix. Some examples are\n",
    "    \n",
    "- Transitive clousure of graph \n",
    "- All pair shortest path problem\n",
    "\n",
    "## Standard `import` statement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from openanalysis.matrix_animator import MatrixAnimator\n",
    "import numpy as np       # Needed to work with arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation Notes\n",
    "\n",
    "- The algorithm should be implemented as a method\n",
    "- The algorithm works on a `networkx` graph\n",
    "- Obtain the adjacancy matrix as follws\n",
    "    \n",
    "```python\n",
    "    def algorithm_name(G):\n",
    "        import networkx as nx\n",
    "        M = nx.to_numpy_matrix(G)\n",
    "        # do other work now\n",
    "```\n",
    "- If Graph is weighted, matrix elements are weights. Default weight for an edge is 1. If an edge doesn't exsist, its weight will be treated as 0. When working with weighted graphs, You have to **MANUALLY** set those weigthts to infinity. \n",
    "\n",
    "```python\n",
    "        m, n = M.shape\n",
    "        for i in range(0, n):\n",
    "            for j in range(0, n):\n",
    "                if i != j and D[i, j] == 0:\n",
    "                   M[i, j] = float('inf')\n",
    "```\n",
    "\n",
    "- After each change in matrix, yield matrix, `yield` copy of current version of matrix, along with a tuple containing current 3 co-ordinates at which change is caused\n",
    "\n",
    "```python\n",
    "     yield np.array(D), (i, j, k)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example Warshall- Floyd  Algorithm\n",
    "\n",
    "Warshal-Floyd Algorithm computes All Pair Shortest Paths of a Graph using its adjacancy matrix\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, Let's implement the algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Floyd_Warshall(G):                # Must have signature like this\n",
    "    D = nx.to_numpy_matrix(G)         # Obtaining Adj. matrix\n",
    "    m, n = D.shape\n",
    "    for i in range(0, n):             # Making non-diagonal zeros to infinity, as it is a Weighted Graph\n",
    "        for j in range(0, n):\n",
    "            if i != j and D[i, j] == 0:\n",
    "                D[i, j] = float('inf')\n",
    "    yield np.array(D), (0, 0, 0)      # Starting yield\n",
    "    count = 0\n",
    "    for k in range(0, n):\n",
    "        for i in range(0, n):\n",
    "            for j in range(0, n):\n",
    "                if D[i, j] > D[i, k] + D[k, j]:\n",
    "                    yield np.array(D), (i, j, k)  # yield as array changes\n",
    "                    D[i, j] = D[i, k] + D[k, j]\n",
    "                count += 1\n",
    "    yield np.array(D), (0, 0, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Algorithm - `MatrixAnimator` class\n",
    "\n",
    "- `__init__(self, fn, G):` \n",
    "    - `fn` : A function yielding matrix along with 3-tuple\n",
    "    - `G`  : Graph on which `fn` has to be applied and visualized\n",
    "\n",
    "\n",
    "- `animate(self, save=False):`\n",
    "    - `save` is `True` implies animation is saved in `output/` folder\n",
    "\n",
    "\n",
    "- `apply_to_graph(self, show_graph=True):`\n",
    "    - applies `self.fn` to `self.G` and displays the result\n",
    "    - `show_graph` is `True` implies Graph is shown along with adjacancy matrix and final matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we shall create a matrix from `numpy` array, and assign random weights to its edges. Then we apply our function to graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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0aCA0NSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwzMrdQMFCw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\nQ2hhciAyNTUgL1N1YnR5cGUgL1R5cGU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       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6cd67707f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "M = nx.from_numpy_matrix(\n",
    "    np.matrix(\n",
    "        [[0, 1, 0, 0, 1, 0],\n",
    "         [1, 0, 1, 0, 1, 0],\n",
    "         [0, 1, 0, 1, 0, 0],\n",
    "         [0, 0, 1, 0, 1, 1],\n",
    "         [1, 1, 0, 1, 0, 0],\n",
    "         [0, 0, 0, 1, 0, 0]]\n",
    "    ))\n",
    "import random\n",
    "for u, v in M.edges():\n",
    "    M.edge[u][v]['weight'] = random.randint(1, 10)\n",
    "animator = MatrixAnimator(Floyd_Warshall, M)\n",
    "animator.apply_to_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After executing\n",
    "\n",
    "    animator.animate(save=True)\n",
    "\n",
    "go to `output/` directory to see the `mp4` files"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example File\n",
    "\n",
    "You can see more examples at [Github](https://github.com/OpenWeavers/openanalysis/blob/master/analysistest/matrix_dp.py)"
   ]
  }
 ],
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