_doc/notebooks/Graphe_et_Map_Reduce.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Graphes et Map Reduce"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On suppose qu'on a un graphe $G(V,E)$ pour lequel on cherche \u00e0 d\u00e9terminer la distance de tous les noeuds \u00e0 un noeud pr\u00e9cis du graphe. Si calculer cette distance pour un graphe de petite taille ne pose pas de probl\u00e8me, pour un grand graphe, cela peut se r\u00e9v\u00e9ler plus complexe. L'id\u00e9e de cet exercice est de montrer que les concepts Map Reduce ne sont pas bien adapt\u00e9s \u00e0 cela. Pour un grand graphe (plusieurs dizaines de millions de noeuds), le calcul est soit trop long \u00e0 faire sur un seul ordinateur, soit cet ordinateur ne peut tout simplement pas contenir tout le graphe. Il faut alors r\u00e9partir ce calcul sur plusieurs machines. Mais commen\u00e7ons d'abord par un graphe simple et sym\u00e9trique : si on peut passer d'un noeud $v$ \u00e0 $v'$, le chemin en sens inverse est possible."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import networkx as nx\n",
      "import random\n",
      "G = nx.Graph()\n",
      "G.add_edge(0,5)\n",
      "n = 15\n",
      "for i in range(0,30):\n",
      "    a,b = random.randint(0,n),random.randint(0,n)\n",
      "    G.add_edge(b,a)\n",
      "pos=nx.spring_layout(G)\n",
      "nx.draw(G,pos,node_color='#A0CBE2')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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U5OZAtgHvuNXY6AhEBj+By5k73zZU0PJllZYgLTkJSUlJ0NXV/aMnnaCHrb6Ny338+DHW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\nl4iISGT/H37/zgKSboWhAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Par exemple, les noeuds 0 et 5 sont reli\u00e9s par un arc. Leur distance est donc de 1. Mais tous les noeuds ne sont pas directement reli\u00e9s entre eux. Il faut parfois emprunter deux ou trois arcs pour passer du noeud 0 \u00e0 un autre. On calculer cette distance minimale $d(v,v')$ o\u00f9 $v$ et $v'$ sont deux noeuds du graphe. Par exemple, partons du noeud 0 et explorons de proche en proche le graphe. Au d\u00e9but, tout ce qu'on conna\u00eet est :\n",
      "\n",
      "$$\\left\\{\\begin{array}{l}d(0,0) = 0 \\\\ \\forall v, \\; d(0,v) = \\infty \\end{array} \\right .$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour \u00e9viter les \u00e9critures trop longues, on note par la suite $d(0,i)=d(i)$. Le calcul est identique quelque soit le noeud. Un algorithme simple consiste \u00e0 mettre \u00e0 jour ce tableau jusqu'\u00e0 ce qu'il n'\u00e9volue plus. Une mise \u00e0 jour consiste \u00e0 prendre un \u00e9l\u00e9ment du tableau, par exemple $d(i)$ et un arc $d(i,j)$ pour mettre \u00e0 jour $d(j)$. On sait alors que $d(j) \\leq d(i)+1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def enumerate_arcs(G):\n",
      "    for i,j in G.edges():\n",
      "        yield i,j\n",
      "        yield j,i\n",
      "d = { 0:0 }\n",
      "maj = 1\n",
      "while maj > 0:\n",
      "    maj = 0\n",
      "    for i,j in enumerate_arcs(G):\n",
      "        if i in d:\n",
      "            x = d[i] + 1\n",
      "            if j in d: \n",
      "                if d[j] > x :\n",
      "                    d[j] = x\n",
      "                    maj += 1\n",
      "            else:\n",
      "                d[j] = x\n",
      "                maj += 1\n",
      "labels={ g:\"d({0})={1}\".format(g,d[g]) for g in G.nodes() }\n",
      "plt.figure(figsize=(12,4))\n",
      "nx.draw(G,pos,node_color='#A0CBE2', labels=labels, node_size=2000,font_size=10)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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eRbYWGxvLb7/9xoFDf+Ln78/D+/exq+xAKdsKmFrkJY+JKYmqBBJiY3h4J5h7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\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Chaque valeur indique la distance d'un noeud au noeud 0. Dans ce graphe, il faut passer par trois arcs au maximum pour aller du noeud 0 \u00e0 n'importe quel autre noeud."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b>Map Reduce</b>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L'algorithme pr\u00e9c\u00e9dent a un co\u00fbt proportionnel au nombre d'it\u00e9rations multipli\u00e9 par le nombre d'arcs et l'acc\u00e8s au dictionnaire <tt>d</tt>, soit au pire $O(|G||E|\\ln_2|G|)$ o\u00f9 $|x|$ est le nombre d'\u00e9l\u00e9ments de cet ensemble. Au pire le plus grand chemin ne peut exc\u00e9der le nombre de noeuds. L'autre caract\u00e9ristique de cet algorithme est qu'il fait intervenir deux ensembles : les arcs <tt>E=G.edges()</tt> et le tableau <tt>d</tt>. Ce qu'il est important de retenir est que chaque it\u00e9ration requiert l'acc\u00e8s \u00e0 tous les \u00e9l\u00e9ments du tableau <tt>d</tt>. Or, pour des grands graphes, <tt>d</tt> est trop grand pour qu'on puisse acc\u00e9der \u00e0 tous ses \u00e9l\u00e9ments \u00e0 la fois. Il faut r\u00e9partir <tt>d</tt> sur plusieurs machines."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lorsqu'on \u00e9voque Map Reduce, une des technologies open source les plus utilis\u00e9es aujourd'hui est <a href=\"http://fr.wikipedia.org/wiki/Hadoop\">Hadoop</a> et un langage associ\u00e9 <a href=\"http://en.wikipedia.org/wiki/Pig_%28programming_tool%29\">PIG</a>. Je ne d\u00e9taillerai pas le langage mais il faut retenir que sa logique est proche du <a href=\"http://fr.wikipedia.org/wiki/Structured_Query_Language\">SQL</a> et qu'on ne peut pas utiliser d'<a href=\"http://fr.wikipedia.org/wiki/Index_(base_de_donn%C3%A9es)\">index</a>. Comment impl\u00e9menter l'algorithme pr\u00e9c\u00e9dent en SQL en partant du principe que l'ensemble des arcs $E$ et du tableau $d$ sont des tables, qu'on peut les parcourir mais qu'on ne peut plus acc\u00e9der \u00e0 un \u00e9l\u00e9ment en particulier ?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Commen\u00e7ons par importer les arcs du graphe dans une base SQL."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas\n",
      "df = pandas.DataFrame( [ _ for _ in enumerate_arcs(G) ], columns=[\"v1\",\"v2\"])\n",
      "df.head(n=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>v1</th>\n",
        "      <th>v2</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0</td>\n",
        "      <td> 4</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 4</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0</td>\n",
        "      <td> 5</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "   v1  v2\n",
        "0   0   4\n",
        "1   4   0\n",
        "2   0   5"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pyensae import Database\n",
      "dbfile = \"graph_arcs.db3\"\n",
      "os.remove(dbfile) # on supprime la pr\u00e9c\u00e9dente base\n",
      "db = Database.fill_sql_table(df, dbfile, \"arc\")\n",
      "db.close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sous Windows, vous pouvez visualiser la base de donn\u00e9es avec le programme <a href=\"http://www.yunqa.de/delphi/doku.php/products/sqlitespy/index\">SQLiteSpy</a>. Il ne reste plus qu'\u00e0 \u00e9crire l'algorithme en SQL en s'inspirant de celui d\u00e9j\u00e0 \u00e9crit en Python. L'instruction <tt>for</tt> est remplac\u00e9e par une instruction <tt>SELECT</tt>, l'instruction <tt>if j in d:</tt> le sera par une instruction <tt>INNER JOIN</tt>. Par exemple, la requ\u00eate suivante retourne les colonnes <tt>v1,v2,v3</tt>. $v1 \\longrightarrow v3$ sont des paires pour lesquelles $d(v1,v3) \\leq 2$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def nolog (*l,**p):pass\n",
      "db = Database(dbfile, LOG = nolog)\n",
      "db.connect()\n",
      "sql = \"\"\"\n",
      "        SELECT A.v1,A.v2,B.v2 AS v3 \n",
      "        FROM arc AS A INNER JOIN arc AS B\n",
      "        ON A.v2 == B.v1\n",
      "        \"\"\"\n",
      "db.execute_view(sql)[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[(0, 4, 0), (0, 4, 5), (0, 4, 7), (0, 4, 12), (4, 0, 4)]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Et la requ\u00eate suivante contient toutes les paires de noeuds $v1,v2$ tels que $d(v1,v2) \\leq 2$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sql = \"\"\"\n",
      "        SELECT A.v1,B.v2 AS v2 FROM arc AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "        UNION ALL \n",
      "        SELECT v1,v2 FROM arc\n",
      "        UNION ALL\n",
      "        SELECT v1,v1 FROM arc\n",
      "        \"\"\"\n",
      "db.execute_view(sql)[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "[(0, 0), (0, 6), (0, 9), (0, 10), (8, 5)]"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Et maintenant on ajoute la distance puis on r\u00e9cup\u00e8re la distance minimale pour chaque paire de noeuds :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sql = \"\"\"\n",
      "        SELECT v1,v2,MIN(d) AS d FROM (\n",
      "            SELECT A.v1,B.v2 AS v2, 2 AS d FROM arc AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "            UNION ALL \n",
      "            SELECT v1,v2, 1 AS d FROM arc\n",
      "            UNION ALL\n",
      "            SELECT v1,v1, 0 AS d FROM arc\n",
      "        )\n",
      "        GROUP BY v1,v2\n",
      "        \"\"\"\n",
      "db.execute_view(sql)[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[(0, 0, 0), (0, 4, 1), (0, 5, 1), (0, 7, 1), (0, 8, 2)]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La distance maximale trouv\u00e9e avec le premier algorithme est sup\u00e9rieure \u00e0 3, il faut donc ajouter une it\u00e9ration. Avant, on cr\u00e9e une <i>VIEW</i> pour \u00e9viter de recopier trop de code SQL :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "db.execute (\"\"\"\n",
      "        CREATE VIEW iter1 AS \n",
      "            SELECT v1,v2,MIN(d) AS d FROM (\n",
      "                SELECT A.v1,B.v2 AS v2, 2 AS d FROM arc AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "                UNION ALL \n",
      "                SELECT v1,v2, 1 AS d FROM arc\n",
      "                UNION ALL\n",
      "                SELECT v1,v1, 0 AS d FROM arc\n",
      "            )\n",
      "            GROUP BY v1,v2\n",
      "        \"\"\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<sqlite3.Cursor at 0x77dfce0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L'it\u00e9ration suivante est presque identique \u00e0 la pr\u00e9c\u00e9dente. On remplace une des tables <tt>arc</tt> par <tt>iter1</tt> puis on ne garde que les distances relatives au noeud 0 :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sql = \"\"\"\n",
      "            SELECT v1,v2,MIN(d) AS d FROM (\n",
      "                SELECT A.v1,B.v2 AS v2, 2 AS d FROM iter1 AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "                UNION ALL \n",
      "                SELECT v1,v2, d FROM iter1\n",
      "            )\n",
      "            GROUP BY v1,v2 \n",
      "            HAVING v1 == 0\n",
      "        \"\"\"\n",
      "db.execute_view(sql)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[(0, 0, 0),\n",
        " (0, 2, 2),\n",
        " (0, 4, 1),\n",
        " (0, 5, 1),\n",
        " (0, 6, 2),\n",
        " (0, 7, 1),\n",
        " (0, 8, 2),\n",
        " (0, 10, 2),\n",
        " (0, 11, 2),\n",
        " (0, 12, 2),\n",
        " (0, 13, 2),\n",
        " (0, 14, 2),\n",
        " (0, 15, 2)]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On ajoute des it\u00e9rations :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "db.execute (\"\"\"CREATE VIEW iter2 AS \n",
      "            SELECT v1,v2,MIN(d) AS d FROM (\n",
      "                SELECT A.v1,B.v2 AS v2, A.d+1 AS d FROM iter1 AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "                UNION ALL \n",
      "                SELECT v1,v2, d FROM iter1\n",
      "            )\n",
      "            GROUP BY v1,v2 ;\"\"\")\n",
      "db.execute (\"\"\"CREATE VIEW iter3 AS \n",
      "            SELECT v1,v2,MIN(d) AS d FROM (\n",
      "                SELECT A.v1,B.v2 AS v2, A.d+1 AS d FROM iter2 AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "                UNION ALL \n",
      "                SELECT v1,v2, d FROM iter2\n",
      "            )\n",
      "            GROUP BY v1,v2 ;\"\"\")\n",
      "db.execute (\"\"\"CREATE VIEW iter4 AS \n",
      "            SELECT v1,v2,MIN(d) AS d FROM (\n",
      "                SELECT A.v1,B.v2 AS v2, A.d+1 AS d FROM iter3 AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "                UNION ALL \n",
      "                SELECT v1,v2, d FROM iter3\n",
      "            )\n",
      "            GROUP BY v1,v2 ;\"\"\")\n",
      "\n",
      "sql = \"\"\"\n",
      "            SELECT v1,v2,MIN(d) AS d FROM (\n",
      "                SELECT A.v1,B.v2 AS v2, A.d+1 AS d FROM iter4 AS A INNER JOIN arc AS B ON A.v2 == B.v1\n",
      "                UNION ALL \n",
      "                SELECT v1,v2, d FROM iter4\n",
      "            )\n",
      "            GROUP BY v1,v2 \n",
      "            HAVING v1 == 0\n",
      "        \"\"\"\n",
      "db.execute_view(sql)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[(0, 0, 0),\n",
        " (0, 1, 5),\n",
        " (0, 2, 3),\n",
        " (0, 3, 4),\n",
        " (0, 4, 1),\n",
        " (0, 5, 1),\n",
        " (0, 6, 3),\n",
        " (0, 7, 1),\n",
        " (0, 8, 2),\n",
        " (0, 9, 6),\n",
        " (0, 10, 2),\n",
        " (0, 11, 3),\n",
        " (0, 12, 2),\n",
        " (0, 13, 2),\n",
        " (0, 14, 3),\n",
        " (0, 15, 2)]"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Il suffit de cr\u00e9er autant de VIEW que d'it\u00e9rations. Mais ce m\u00e9canisme appara\u00eet moins souple que la version impl\u00e9ment\u00e9e en langage Python. La premi\u00e8re difficult\u00e9 est le nombre d'it\u00e9rations qui n'est pas connu \u00e0 l'avance. Avec le langage SQL, ce nombre d'it\u00e9rations ne peut pas d\u00e9pendre des donn\u00e9es. Il en est de m\u00eame avec un langage Map Reduce.\n",
      "\n",
      "En revanche, il est plus facile de parall\u00e9liser la version SQL sur plusieurs machines car une requ\u00eate SQL s'y pr\u00eate bien. Les probl\u00e8mes de parall\u00e9lisation surviennent g\u00e9n\u00e9ralement si le graphe est tr\u00e8s connect\u00e9 : l'instruction <tt>INNER JOIN</tt> a un co\u00fbt inf\u00e9rieur \u00e0 $O(|E||G|^2)$. Cette valeur est sup\u00e9rieure au co\u00fbt de l'algorithme cod\u00e9 en Python car il est r\u00e9alis\u00e9 sans index. Moins il y a d'arcs, plus c'est rapide. \n",
      "\n",
      "Cependant, dans les faits, on remarque qu'il suffit qu'un petit nombre de noeuds soient connect\u00e9s \u00e0 beaucoup d'autres pour que des probl\u00e8mes de parall\u00e9lisation surviennent. En r\u00e8gle g\u00e9n\u00e9rale, chaque machine re\u00e7oit toutes les donn\u00e9es qui partagent la m\u00eame cl\u00e9 utilis\u00e9e dans l'instruction <tt>INNER JOIN</tt>. Si la quantit\u00e9 de donn\u00e9es associ\u00e9e \u00e0 une cl\u00e9 est tr\u00e8s grande, il est possible que la machine traitant les donn\u00e9es de cette cl\u00e9 termine son ex\u00e9cution bien plus tard que toutes les autres. \n",
      "\n",
      "C'est dans ce cas qu'il faut parfois user d'imagination."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}