class02b_storage_R.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": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘igraph’\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    decompose, spectrum\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:base’:\n",
      "\n",
      "    union\n",
      "\n",
      "\n"
     ]
    }
   ],
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "enumerate_matrix <- function(gmat, i) {\n",
    "    which(gmat[i, ] == 1)\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": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "enumerate_adj_list <- function(adj_list, i) {\n",
    "    adj_list[[i]]\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": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "enumerate_edge_list <- function(edge_list, i) {\n",
    "    inds1 <- which(edge_list[,1] == i)\n",
    "    inds2 <- which(edge_list[,2] == i)\n",
    "    c(edge_list[inds1,2], edge_list[inds2,1])\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This next function is the simulation funtion.  \"n\" is the number of vertices.\n",
    "It returns a length-three list containing the average running time for enumerating the neighbor vertices of a vertex in the graph. \n",
    "\n",
    "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": 5,
   "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 <- sample_pa(n, out.seq=rep(5, n), directed=FALSE)\n",
    "                         \n",
    "                         g_matrix <- as.matrix(as_adjacency_matrix(g))\n",
    "                         g_adj_list <- as_adj_list(g)\n",
    "                         g_edge_list <- as_edgelist(g)\n",
    "\n",
    "                         time_mat <- system.time(\n",
    "                             replicate(nsubrep, {\n",
    "                                 lapply(1:n,\n",
    "                                        function(i) {\n",
    "                                            enumerate_matrix(g_matrix, i)\n",
    "                                        })\n",
    "                             })\n",
    "                         )[1]\n",
    "                         \n",
    "                         time_adj_list <- system.time(\n",
    "                             replicate(nsubrep, {\n",
    "                                 lapply(1:n,\n",
    "                                        function(i) {\n",
    "                                            enumerate_adj_list(g_adj_list, i)\n",
    "                                        })\n",
    "                             })\n",
    "                         )[1]\n",
    "                         \n",
    "                         time_edge_list <- system.time(\n",
    "                             replicate(nsubrep, {\n",
    "                                 lapply(1:n,\n",
    "                                        function(i) {\n",
    "                                            enumerate_edge_list(g_edge_list, 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": 16,
   "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": 17,
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.0529999999999973</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.0130000000000336</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.146999999999991</dd>\n",
       "</dl>\n",
       "</li>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.0653333333333421</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.0156666666666467</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.282666666666671</dd>\n",
       "</dl>\n",
       "</li>\n",
       "\t<li><dl class=dl-horizontal>\n",
       "\t<dt>matrix</dt>\n",
       "\t\t<dd>0.0875999999999976</dd>\n",
       "\t<dt>adjlist</dt>\n",
       "\t\t<dd>0.0153999999999883</dd>\n",
       "\t<dt>edgelist</dt>\n",
       "\t\t<dd>0.451399999999984</dd>\n",
       "</dl>\n",
       "</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate}\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.0529999999999973\n",
       "\\item[adjlist] 0.0130000000000336\n",
       "\\item[edgelist] 0.146999999999991\n",
       "\\end{description*}\n",
       "\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.0653333333333421\n",
       "\\item[adjlist] 0.0156666666666467\n",
       "\\item[edgelist] 0.282666666666671\n",
       "\\end{description*}\n",
       "\n",
       "\\item \\begin{description*}\n",
       "\\item[matrix] 0.0875999999999976\n",
       "\\item[adjlist] 0.0153999999999883\n",
       "\\item[edgelist] 0.451399999999984\n",
       "\\end{description*}\n",
       "\n",
       "\\end{enumerate}\n"
      ],
      "text/markdown": [
       "1. matrix\n",
       ":   0.0529999999999973adjlist\n",
       ":   0.0130000000000336edgelist\n",
       ":   0.146999999999991\n",
       "\n",
       "\n",
       "2. matrix\n",
       ":   0.0653333333333421adjlist\n",
       ":   0.0156666666666467edgelist\n",
       ":   0.282666666666671\n",
       "\n",
       "\n",
       "3. matrix\n",
       ":   0.0875999999999976adjlist\n",
       ":   0.0153999999999883edgelist\n",
       ":   0.451399999999984\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[[1]]\n",
       "  matrix  adjlist edgelist \n",
       "   0.053    0.013    0.147 \n",
       "\n",
       "[[2]]\n",
       "    matrix    adjlist   edgelist \n",
       "0.06533333 0.01566667 0.28266667 \n",
       "\n",
       "[[3]]\n",
       "  matrix  adjlist edgelist \n",
       "  0.0876   0.0154   0.4514 \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": 19,
   "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 3 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>network_size</th><th scope=col>matrix</th><th scope=col>adjlist</th><th scope=col>edgelist</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>100</td><td>0.05300000</td><td>0.01300000</td><td>0.1470000</td></tr>\n",
       "\t<tr><td>300</td><td>0.06533333</td><td>0.01566667</td><td>0.2826667</td></tr>\n",
       "\t<tr><td>500</td><td>0.08760000</td><td>0.01540000</td><td>0.4514000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       " network\\_size & matrix & adjlist & edgelist\\\\\n",
       " <fct> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 100 & 0.05300000 & 0.01300000 & 0.1470000\\\\\n",
       "\t 300 & 0.06533333 & 0.01566667 & 0.2826667\\\\\n",
       "\t 500 & 0.08760000 & 0.01540000 & 0.4514000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 4\n",
       "\n",
       "| network_size &lt;fct&gt; | matrix &lt;dbl&gt; | adjlist &lt;dbl&gt; | edgelist &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 100 | 0.05300000 | 0.01300000 | 0.1470000 |\n",
       "| 300 | 0.06533333 | 0.01566667 | 0.2826667 |\n",
       "| 500 | 0.08760000 | 0.01540000 | 0.4514000 |\n",
       "\n"
      ],
      "text/plain": [
       "  network_size matrix     adjlist    edgelist \n",
       "1 100          0.05300000 0.01300000 0.1470000\n",
       "2 300          0.06533333 0.01566667 0.2826667\n",
       "3 500          0.08760000 0.01540000 0.4514000"
      ]
     },
     "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": 21,
   "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 9 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>network_size</th><th scope=col>variable</th><th scope=col>value</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>100</td><td>matrix  </td><td>0.05300000</td></tr>\n",
       "\t<tr><td>300</td><td>matrix  </td><td>0.06533333</td></tr>\n",
       "\t<tr><td>500</td><td>matrix  </td><td>0.08760000</td></tr>\n",
       "\t<tr><td>100</td><td>adjlist </td><td>0.01300000</td></tr>\n",
       "\t<tr><td>300</td><td>adjlist </td><td>0.01566667</td></tr>\n",
       "\t<tr><td>500</td><td>adjlist </td><td>0.01540000</td></tr>\n",
       "\t<tr><td>100</td><td>edgelist</td><td>0.14700000</td></tr>\n",
       "\t<tr><td>300</td><td>edgelist</td><td>0.28266667</td></tr>\n",
       "\t<tr><td>500</td><td>edgelist</td><td>0.45140000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 9 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " network\\_size & variable & value\\\\\n",
       " <fct> & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 100 & matrix   & 0.05300000\\\\\n",
       "\t 300 & matrix   & 0.06533333\\\\\n",
       "\t 500 & matrix   & 0.08760000\\\\\n",
       "\t 100 & adjlist  & 0.01300000\\\\\n",
       "\t 300 & adjlist  & 0.01566667\\\\\n",
       "\t 500 & adjlist  & 0.01540000\\\\\n",
       "\t 100 & edgelist & 0.14700000\\\\\n",
       "\t 300 & edgelist & 0.28266667\\\\\n",
       "\t 500 & edgelist & 0.45140000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 9 × 3\n",
       "\n",
       "| network_size &lt;fct&gt; | variable &lt;fct&gt; | value &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 100 | matrix   | 0.05300000 |\n",
       "| 300 | matrix   | 0.06533333 |\n",
       "| 500 | matrix   | 0.08760000 |\n",
       "| 100 | adjlist  | 0.01300000 |\n",
       "| 300 | adjlist  | 0.01566667 |\n",
       "| 500 | adjlist  | 0.01540000 |\n",
       "| 100 | edgelist | 0.14700000 |\n",
       "| 300 | edgelist | 0.28266667 |\n",
       "| 500 | edgelist | 0.45140000 |\n",
       "\n"
      ],
      "text/plain": [
       "  network_size variable value     \n",
       "1 100          matrix   0.05300000\n",
       "2 300          matrix   0.06533333\n",
       "3 500          matrix   0.08760000\n",
       "4 100          adjlist  0.01300000\n",
       "5 300          adjlist  0.01566667\n",
       "6 500          adjlist  0.01540000\n",
       "7 100          edgelist 0.14700000\n",
       "8 300          edgelist 0.28266667\n",
       "9 500          edgelist 0.45140000"
      ]
     },
     "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAACXBIWXMAABJ0AAASdAHeZh94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\nAJgQOwCACbEDAJgQOwCACbEDAJgIZ2oZ6uJ4EZEAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "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
}