class02b_storage_R_template.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class Session 4 Exercise:\n",
    "## Comparing asymptotic running time for enumerating neighbors of all vertices in a graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will measure the running time for enumerating the neighbor vertices for three different data structures for representing the graph:\n",
    "    adjacency matrix\n",
    "    adjacency list\n",
    "    edge list\n",
    "    \n",
    "First, we import all the R packages that we will need for this exercise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "library(igraph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function that enumerates the neighbors of a vertex i, when the \n",
    "graph is stored in adjacency matrix format (ones and zeroes).  Use the `which` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "enumerate_matrix <- function(gmat, i) {\n",
    "    FILL IN HERE\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function that enumerates the neighbors of a vertex i, when the \n",
    "graph is stored in adjacency list format. Use the `[[` function (i..e, array indexing)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "enumerate_adj_list <- function(adj_list, i) {\n",
    "    FILL IN HERE\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function that enumerates the neighbors of a vertex i, when the \n",
    "graph is stored in edge-list format.  Use the `which` function and then the `c` (concatenate) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "enumerate_edge_list <- function(edge_list, i) {\n",
    "    inds1 <- FILL IN HERE\n",
    "    inds2 <- FILL IN HERE\n",
    "    c(edge_list[inds1,2], edge_list[inds2,1])\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This next function is the simulation funtion. Use the `sample_pa` function in igraph to generate a Barabasi-Albert (undirected) graph, with n vertices and m=5 (which should have number of edges equal to nm - m^2 / 2 - m/2).\n",
    "It returns a length-three list containing the average running time for enumerating the neighbor vertices of a vertex in the graph. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "dosim <- function(n) {\n",
    "\n",
    "    nrep <- 10\n",
    "    nsubrep <- 10\n",
    "    \n",
    "    simdf <- do.call(rbind,\n",
    "                     replicate(nrep, {\n",
    "                        # make a random undirected graph with fixed (average) vertex degree = 5\n",
    "                         g <- FILL IN HERE\n",
    "                         \n",
    "                         g_matrix <- # use igraph as_adjacency_matrix and then R as.matrix\n",
    "                         g_adj_list <- # use igraph as_adj_list\n",
    "                         g_edge_list <- # use igraph as_edgelist\n",
    "\n",
    "                         time_mat <- system.time(\n",
    "                             replicate(nsubrep, {\n",
    "                                 lapply(1:n,\n",
    "                                        function(i) {\n",
    "                                            # call enumerate_matrix for g_matrix and vertex i\n",
    "                                        })\n",
    "                             })\n",
    "                         )[1]\n",
    "                         \n",
    "                         time_adj_list <- system.time(\n",
    "                             replicate(nsubrep, {\n",
    "                                 lapply(1:n,\n",
    "                                        function(i) {\n",
    "                                            # call enumerate_adj_list for g_matrix and vertex i                                            \n",
    "                                        })\n",
    "                             })\n",
    "                         )[1]\n",
    "                         \n",
    "                         time_edge_list <- system.time(\n",
    "                             replicate(nsubrep, {\n",
    "                                 lapply(1:n,\n",
    "                                        function(i) {\n",
    "                                            # call enumerate_edge_list for g_matrix and vertex i                                                \n",
    "                                        })\n",
    "                             })\n",
    "                         )[1]\n",
    "\n",
    "                         rowdf <- data.frame(matrix=time_mat,\n",
    "                                             adjlist=time_adj_list,\n",
    "                                             edgelist=time_edge_list)\n",
    "                         \n",
    "                         rowdf\n",
    "                     }, simplify=FALSE)\n",
    "                     )\n",
    "    \n",
    "    # average over replicates\n",
    "    simres <- apply(simdf, 2, mean)\n",
    "    \n",
    "    # divide by n so that the running time results are on a per-vertex basis\n",
    "    simres/n\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the function for the graphs of 100, 300, and 500 vertices, and gather the results in a list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "nvals <- c(100, 300, 500)\n",
    "sim_data_list <- lapply(nvals, dosim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rescale the list to make the numbers in milliseconds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_data_list_rescaled <- lapply(sim_data_list, function(v) {v*1000})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the data in the list format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.0287599999999975</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.00176000000000386</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.18432</dd>\n",
       "</dl>\n",
       "</li>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.0696000000000026</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.00171999999999798</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.353239999999998</dd>\n",
       "</dl>\n",
       "</li>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.10284</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.00173333333332721</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.516826666666667</dd>\n",
       "</dl>\n",
       "</li>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.138470000000001</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.00184999999999832</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.675100000000001</dd>\n",
       "</dl>\n",
       "</li>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.168968</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.00185600000000068</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.806472</dd>\n",
       "</dl>\n",
       "</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate}\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.0287599999999975\n",
       "\\item[adjlist] 0.00176000000000386\n",
       "\\item[edgelist] 0.18432\n",
       "\\end{description*}\n",
       "\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.0696000000000026\n",
       "\\item[adjlist] 0.00171999999999798\n",
       "\\item[edgelist] 0.353239999999998\n",
       "\\end{description*}\n",
       "\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.10284\n",
       "\\item[adjlist] 0.00173333333332721\n",
       "\\item[edgelist] 0.516826666666667\n",
       "\\end{description*}\n",
       "\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.138470000000001\n",
       "\\item[adjlist] 0.00184999999999832\n",
       "\\item[edgelist] 0.675100000000001\n",
       "\\end{description*}\n",
       "\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.168968\n",
       "\\item[adjlist] 0.00185600000000068\n",
       "\\item[edgelist] 0.806472\n",
       "\\end{description*}\n",
       "\n",
       "\\end{enumerate}\n"
      ],
      "text/markdown": [
       "1. matrix\n",
       ":   0.0287599999999975adjlist\n",
       ":   0.00176000000000386edgelist\n",
       ":   0.18432\n",
       "\n",
       "\n",
       "2. matrix\n",
       ":   0.0696000000000026adjlist\n",
       ":   0.00171999999999798edgelist\n",
       ":   0.353239999999998\n",
       "\n",
       "\n",
       "3. matrix\n",
       ":   0.10284adjlist\n",
       ":   0.00173333333332721edgelist\n",
       ":   0.516826666666667\n",
       "\n",
       "\n",
       "4. matrix\n",
       ":   0.138470000000001adjlist\n",
       ":   0.00184999999999832edgelist\n",
       ":   0.675100000000001\n",
       "\n",
       "\n",
       "5. matrix\n",
       ":   0.168968adjlist\n",
       ":   0.00185600000000068edgelist\n",
       ":   0.806472\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[[1]]\n",
       "  matrix  adjlist edgelist \n",
       " 0.02876  0.00176  0.18432 \n",
       "\n",
       "[[2]]\n",
       "  matrix  adjlist edgelist \n",
       " 0.06960  0.00172  0.35324 \n",
       "\n",
       "[[3]]\n",
       "     matrix     adjlist    edgelist \n",
       "0.102840000 0.001733333 0.516826667 \n",
       "\n",
       "[[4]]\n",
       "  matrix  adjlist edgelist \n",
       " 0.13847  0.00185  0.67510 \n",
       "\n",
       "[[5]]\n",
       "  matrix  adjlist edgelist \n",
       "0.168968 0.001856 0.806472 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_data_list_rescaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert the list to a wide data frame, using do.call and rbind; make the network size the first column of the data frame (and as a factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_data_list_df <- data.frame(network_size=as.factor(nvals),\n",
    "                               do.call(rbind, sim_data_list_rescaled))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the wide data frame format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>network_size</th><th scope=col>matrix</th><th scope=col>adjlist</th><th scope=col>edgelist</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1000       </td><td>0.028760   </td><td>0.001760000</td><td>0.1843200  </td></tr>\n",
       "\t<tr><td>2000       </td><td>0.069600   </td><td>0.001720000</td><td>0.3532400  </td></tr>\n",
       "\t<tr><td>3000       </td><td>0.102840   </td><td>0.001733333</td><td>0.5168267  </td></tr>\n",
       "\t<tr><td>4000       </td><td>0.138470   </td><td>0.001850000</td><td>0.6751000  </td></tr>\n",
       "\t<tr><td>5000       </td><td>0.168968   </td><td>0.001856000</td><td>0.8064720  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " network\\_size & matrix & adjlist & edgelist\\\\\n",
       "\\hline\n",
       "\t 1000        & 0.028760    & 0.001760000 & 0.1843200  \\\\\n",
       "\t 2000        & 0.069600    & 0.001720000 & 0.3532400  \\\\\n",
       "\t 3000        & 0.102840    & 0.001733333 & 0.5168267  \\\\\n",
       "\t 4000        & 0.138470    & 0.001850000 & 0.6751000  \\\\\n",
       "\t 5000        & 0.168968    & 0.001856000 & 0.8064720  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "  network_size matrix   adjlist     edgelist \n",
       "1 1000         0.028760 0.001760000 0.1843200\n",
       "2 2000         0.069600 0.001720000 0.3532400\n",
       "3 3000         0.102840 0.001733333 0.5168267\n",
       "4 4000         0.138470 0.001850000 0.6751000\n",
       "5 5000         0.168968 0.001856000 0.8064720"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_data_list_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"Melt\" the data into a narrow format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(dplyr)\n",
    "library(reshape2)\n",
    "sim_data_list_melted <- melt(sim_data_list_df, id.vars=\"network_size\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the narrow data frame format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>network_size</th><th scope=col>variable</th><th scope=col>value</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1000       </td><td>matrix     </td><td>0.028760000</td></tr>\n",
       "\t<tr><td>2000       </td><td>matrix     </td><td>0.069600000</td></tr>\n",
       "\t<tr><td>3000       </td><td>matrix     </td><td>0.102840000</td></tr>\n",
       "\t<tr><td>4000       </td><td>matrix     </td><td>0.138470000</td></tr>\n",
       "\t<tr><td>5000       </td><td>matrix     </td><td>0.168968000</td></tr>\n",
       "\t<tr><td>1000       </td><td>adjlist    </td><td>0.001760000</td></tr>\n",
       "\t<tr><td>2000       </td><td>adjlist    </td><td>0.001720000</td></tr>\n",
       "\t<tr><td>3000       </td><td>adjlist    </td><td>0.001733333</td></tr>\n",
       "\t<tr><td>4000       </td><td>adjlist    </td><td>0.001850000</td></tr>\n",
       "\t<tr><td>5000       </td><td>adjlist    </td><td>0.001856000</td></tr>\n",
       "\t<tr><td>1000       </td><td>edgelist   </td><td>0.184320000</td></tr>\n",
       "\t<tr><td>2000       </td><td>edgelist   </td><td>0.353240000</td></tr>\n",
       "\t<tr><td>3000       </td><td>edgelist   </td><td>0.516826667</td></tr>\n",
       "\t<tr><td>4000       </td><td>edgelist   </td><td>0.675100000</td></tr>\n",
       "\t<tr><td>5000       </td><td>edgelist   </td><td>0.806472000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " network\\_size & variable & value\\\\\n",
       "\\hline\n",
       "\t 1000        & matrix      & 0.028760000\\\\\n",
       "\t 2000        & matrix      & 0.069600000\\\\\n",
       "\t 3000        & matrix      & 0.102840000\\\\\n",
       "\t 4000        & matrix      & 0.138470000\\\\\n",
       "\t 5000        & matrix      & 0.168968000\\\\\n",
       "\t 1000        & adjlist     & 0.001760000\\\\\n",
       "\t 2000        & adjlist     & 0.001720000\\\\\n",
       "\t 3000        & adjlist     & 0.001733333\\\\\n",
       "\t 4000        & adjlist     & 0.001850000\\\\\n",
       "\t 5000        & adjlist     & 0.001856000\\\\\n",
       "\t 1000        & edgelist    & 0.184320000\\\\\n",
       "\t 2000        & edgelist    & 0.353240000\\\\\n",
       "\t 3000        & edgelist    & 0.516826667\\\\\n",
       "\t 4000        & edgelist    & 0.675100000\\\\\n",
       "\t 5000        & edgelist    & 0.806472000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "   network_size variable value      \n",
       "1  1000         matrix   0.028760000\n",
       "2  2000         matrix   0.069600000\n",
       "3  3000         matrix   0.102840000\n",
       "4  4000         matrix   0.138470000\n",
       "5  5000         matrix   0.168968000\n",
       "6  1000         adjlist  0.001760000\n",
       "7  2000         adjlist  0.001720000\n",
       "8  3000         adjlist  0.001733333\n",
       "9  4000         adjlist  0.001850000\n",
       "10 5000         adjlist  0.001856000\n",
       "11 1000         edgelist 0.184320000\n",
       "12 2000         edgelist 0.353240000\n",
       "13 3000         edgelist 0.516826667\n",
       "14 4000         edgelist 0.675100000\n",
       "15 5000         edgelist 0.806472000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_data_list_melted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the data.  The \"barchart\" function in lattice graphics is a nice way to plot a grouped bar plot from a narrow data frame. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RkxYsQDDzxwEB4i/6dsYbdt27Zjjjkmebt+/fpLly4NIaSlpV188cXPPfdcKnO0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\nHQDAhNgBAEyIHQDAhNgBAEwEkKfqwJMF5HAAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(lattice)\n",
    "colors = c('red', 'orange', 'yellow')\n",
    "barchart(value~network_size, data=sim_data_list_melted, groups=variable,\n",
    "         auto.key=list(space='right'),\n",
    "        par.settings=list(superpose.polygon=list(col=colors)))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}