Repository: incubator-madlib-site
Updated Branches:
  refs/heads/asf-site 924263246 -> a72096891


graph apsp jupyter notebook


Project: http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/repo
Commit: 
http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/commit/a7209689
Tree: http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/tree/a7209689
Diff: http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/diff/a7209689

Branch: refs/heads/asf-site
Commit: a720968910e7fd694e6b7adecc1834399616994d
Parents: 9242632
Author: Frank McQuillan <fmcquil...@pivotal.io>
Authored: Thu Jun 15 14:29:18 2017 -0700
Committer: Frank McQuillan <fmcquil...@pivotal.io>
Committed: Thu Jun 15 14:29:18 2017 -0700

----------------------------------------------------------------------
 community-artifacts/APSP-v1.ipynb | 2004 ++++++++++++++++++++++++++++++++
 1 file changed, 2004 insertions(+)
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http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/blob/a7209689/community-artifacts/APSP-v1.ipynb
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diff --git a/community-artifacts/APSP-v1.ipynb 
b/community-artifacts/APSP-v1.ipynb
new file mode 100644
index 0000000..05b20b3
--- /dev/null
+++ b/community-artifacts/APSP-v1.ipynb
@@ -0,0 +1,2004 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# All pairs shortest path\n",
+    "The all pairs shortest paths (APSP) algorithm finds the lengths (summed 
weights) of the shortest paths between all pairs of vertices such that the sum 
of the weights of the path edges is minimized.\n",
+    "\n",
+    "APSP was added in MADlib 1.12."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      
"/Users/fmcquillan/anaconda/lib/python2.7/site-packages/IPython/config.py:13: 
ShimWarning: The `IPython.config` package has been deprecated. You should 
import from traitlets.config instead.\n",
+      "  \"You should import from traitlets.config instead.\", ShimWarning)\n",
+      
"/Users/fmcquillan/anaconda/lib/python2.7/site-packages/IPython/utils/traitlets.py:5:
 UserWarning: IPython.utils.traitlets has moved to a top-level traitlets 
package.\n",
+      "  warn(\"IPython.utils.traitlets has moved to a top-level traitlets 
package.\")\n"
+     ]
+    }
+   ],
+   "source": [
+    "%load_ext sql"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "u'Connected: gpdbchina@madlib'"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Greenplum 4.3.10.0\n",
+    "%sql postgresql://gpdbchina@10.194.10.68:61000/madlib\n",
+    "        \n",
+    "# PostgreSQL local\n",
+    "#%sql postgresql://fmcquillan@localhost:5432/madlib\n",
+    "\n",
+    "# Greenplum 4.2.3.0\n",
+    "#%sql postgresql://gpdbchina@10.194.10.68:55000/madlib"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>version</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>MADlib version: 1.12-dev, git revision: 
rel/v1.11-16-gf50f76d, cmake configuration time: Mon Jun 12 20:12:42 UTC 2017, 
build type: Release, build system: Linux-2.6.18-238.27.1.el5.hotfix.bz516490, C 
compiler: gcc 4.4.0, C++ compiler: g++ 4.4.0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(u'MADlib version: 1.12-dev, git revision: rel/v1.11-16-gf50f76d, 
cmake configuration time: Mon Jun 12 20:12:42 UTC 2017, build type: Release, 
build system: Linux-2.6.18-238.27.1.el5.hotfix.bz516490, C compiler: gcc 4.4.0, 
C++ compiler: g++ 4.4.0',)]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%sql select madlib.version();\n",
+    "#%sql select version();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1.  Create vertex and edge tables"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "Done.\n",
+      "Done.\n",
+      "8 rows affected.\n",
+      "12 rows affected.\n",
+      "12 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>src</th>\n",
+       "        <th>dest</th>\n",
+       "        <th>weight</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
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+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 1, 1.0),\n",
+       " (0, 2, 1.0),\n",
+       " (0, 4, 10.0),\n",
+       " (1, 2, 2.0),\n",
+       " (1, 3, 10.0),\n",
+       " (2, 3, 1.0),\n",
+       " (2, 5, 1.0),\n",
+       " (2, 6, 3.0),\n",
+       " (3, 0, 1.0),\n",
+       " (4, 0, -2.0),\n",
+       " (5, 6, 1.0),\n",
+       " (6, 7, 1.0)]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql \n",
+    "DROP TABLE IF EXISTS vertex, edge;\n",
+    "\n",
+    "CREATE TABLE vertex(\n",
+    "        id INTEGER\n",
+    "        );\n",
+    "\n",
+    "CREATE TABLE edge(\n",
+    "        src INTEGER,\n",
+    "        dest INTEGER,\n",
+    "        weight FLOAT8\n",
+    "        );\n",
+    "\n",
+    "INSERT INTO vertex VALUES\n",
+    "(0),\n",
+    "(1),\n",
+    "(2),\n",
+    "(3),\n",
+    "(4),\n",
+    "(5),\n",
+    "(6),\n",
+    "(7);\n",
+    "\n",
+    "INSERT INTO edge VALUES\n",
+    "(0, 1, 1.0),\n",
+    "(0, 2, 1.0),\n",
+    "(0, 4, 10.0),\n",
+    "(1, 2, 2.0),\n",
+    "(1, 3, 10.0),\n",
+    "(2, 3, 1.0),\n",
+    "(2, 5, 1.0),\n",
+    "(2, 6, 3.0),\n",
+    "(3, 0, 1.0),\n",
+    "(4, 0, -2.0),\n",
+    "(5, 6, 1.0),\n",
+    "(6, 7, 1.0);\n",
+    "\n",
+    "SELECT * FROM edge ORDER BY src, dest;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 2.  Calculate the shortest paths"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "64 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>src</th>\n",
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+       "        <td>0</td>\n",
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+       "        <td>1</td>\n",
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+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>6</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>6</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>7</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 0.0, 0),\n",
+       " (0, 1, 1.0, 1),\n",
+       " (0, 2, 1.0, 2),\n",
+       " (0, 3, 2.0, 2),\n",
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+       " (0, 5, 2.0, 2),\n",
+       " (0, 6, 3.0, 5),\n",
+       " (0, 7, 4.0, 6),\n",
+       " (1, 0, 4.0, 3),\n",
+       " (1, 1, 0.0, 1),\n",
+       " (1, 2, 2.0, 2),\n",
+       " (1, 3, 3.0, 2),\n",
+       " (1, 4, 14.0, 0),\n",
+       " (1, 5, 3.0, 2),\n",
+       " (1, 6, 4.0, 5),\n",
+       " (1, 7, 5.0, 6),\n",
+       " (2, 0, 2.0, 3),\n",
+       " (2, 1, 3.0, 0),\n",
+       " (2, 2, 0.0, 2),\n",
+       " (2, 3, 1.0, 3),\n",
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+       " (2, 5, 1.0, 5),\n",
+       " (2, 6, 2.0, 5),\n",
+       " (2, 7, 3.0, 6),\n",
+       " (3, 0, 1.0, 0),\n",
+       " (3, 1, 2.0, 0),\n",
+       " (3, 2, 2.0, 0),\n",
+       " (3, 3, 0.0, 3),\n",
+       " (3, 4, 11.0, 0),\n",
+       " (3, 5, 3.0, 2),\n",
+       " (3, 6, 4.0, 5),\n",
+       " (3, 7, 5.0, 6),\n",
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+       " (4, 5, 0.0, 2),\n",
+       " (4, 6, 1.0, 5),\n",
+       " (4, 7, 2.0, 6),\n",
+       " (5, 0, inf, None),\n",
+       " (5, 1, inf, None),\n",
+       " (5, 2, inf, None),\n",
+       " (5, 3, inf, None),\n",
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+       " (5, 5, 0.0, 5),\n",
+       " (5, 6, 1.0, 6),\n",
+       " (5, 7, 2.0, 6),\n",
+       " (6, 0, inf, None),\n",
+       " (6, 1, inf, None),\n",
+       " (6, 2, inf, None),\n",
+       " (6, 3, inf, None),\n",
+       " (6, 4, inf, None),\n",
+       " (6, 5, inf, None),\n",
+       " (6, 6, 0.0, 6),\n",
+       " (6, 7, 1.0, 7),\n",
+       " (7, 0, inf, None),\n",
+       " (7, 1, inf, None),\n",
+       " (7, 2, inf, None),\n",
+       " (7, 3, inf, None),\n",
+       " (7, 4, inf, None),\n",
+       " (7, 5, inf, None),\n",
+       " (7, 6, inf, None),\n",
+       " (7, 7, 0.0, 7)]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out, out_summary;\n",
+    "\n",
+    "SELECT madlib.graph_apsp(\n",
+    "                         'vertex',      -- Vertex table\n",
+    "                         NULL,          -- Vertix id column (NULL means 
use default naming)\n",
+    "                         'edge',        -- Edge table\n",
+    "                         NULL,          -- Edge arguments (NULL means use 
default naming)\n",
+    "                         'out');        -- Output table of shortest 
paths\n",
+    "\n",
+    "SELECT * FROM out ORDER BY src,dest;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 3.  Get the shortest path from vertex 0 to vertex 5"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "1 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>path</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>[0, 2, 5]</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[([0, 2, 5],)]"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_path;\n",
+    "SELECT madlib.graph_apsp_get_path('out',0,5,'out_path');\n",
+    "SELECT * FROM out_path;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 4.  Custom column names\n",
+    "Now let's do a similar example except using different column names in the 
tables (i.e., not the defaults). Create the vertex and edge tables:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "8 rows affected.\n",
+      "12 rows affected.\n",
+      "12 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>e_src</th>\n",
+       "        <th>dest</th>\n",
+       "        <th>e_weight</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 1, 1.0),\n",
+       " (0, 2, 1.0),\n",
+       " (0, 4, 10.0),\n",
+       " (1, 2, 2.0),\n",
+       " (1, 3, 10.0),\n",
+       " (2, 3, 1.0),\n",
+       " (2, 5, 1.0),\n",
+       " (2, 6, 3.0),\n",
+       " (3, 0, 1.0),\n",
+       " (4, 0, -2.0),\n",
+       " (5, 6, 1.0),\n",
+       " (6, 7, 1.0)]"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql \n",
+    "DROP TABLE IF EXISTS vertex_alt, edge_alt;\n",
+    "CREATE TABLE vertex_alt AS SELECT id AS v_id FROM vertex;\n",
+    "CREATE TABLE edge_alt AS SELECT src AS e_src, dest, weight AS e_weight 
FROM edge;\n",
+    "SELECT * FROM edge_alt ORDER BY e_src, dest;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 5.  Calculate the shortest paths"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "64 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>e_src</th>\n",
+       "        <th>dest</th>\n",
+       "        <th>e_weight</th>\n",
+       "        <th>parent</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
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+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>14.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>6</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>7</td>\n",
+       "        <td>5.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>4</td>\n",
+       "        <td>12.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>6</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>7</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>4</td>\n",
+       "        <td>11.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>6</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>7</td>\n",
+       "        <td>5.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>1</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>2</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>4</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>7</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>7</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>6</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>6</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>7</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 0.0, 0),\n",
+       " (0, 1, 1.0, 1),\n",
+       " (0, 2, 1.0, 2),\n",
+       " (0, 3, 2.0, 2),\n",
+       " (0, 4, 10.0, 4),\n",
+       " (0, 5, 2.0, 2),\n",
+       " (0, 6, 3.0, 5),\n",
+       " (0, 7, 4.0, 6),\n",
+       " (1, 0, 4.0, 3),\n",
+       " (1, 1, 0.0, 1),\n",
+       " (1, 2, 2.0, 2),\n",
+       " (1, 3, 3.0, 2),\n",
+       " (1, 4, 14.0, 0),\n",
+       " (1, 5, 3.0, 2),\n",
+       " (1, 6, 4.0, 5),\n",
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+       " (2, 1, 3.0, 0),\n",
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+       " (2, 7, 3.0, 6),\n",
+       " (3, 0, 1.0, 0),\n",
+       " (3, 1, 2.0, 0),\n",
+       " (3, 2, 2.0, 0),\n",
+       " (3, 3, 0.0, 3),\n",
+       " (3, 4, 11.0, 0),\n",
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+       " (3, 6, 4.0, 5),\n",
+       " (3, 7, 5.0, 6),\n",
+       " (4, 0, -2.0, 0),\n",
+       " (4, 1, -1.0, 0),\n",
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+       " (4, 4, 0.0, 4),\n",
+       " (4, 5, 0.0, 2),\n",
+       " (4, 6, 1.0, 5),\n",
+       " (4, 7, 2.0, 6),\n",
+       " (5, 0, inf, None),\n",
+       " (5, 1, inf, None),\n",
+       " (5, 2, inf, None),\n",
+       " (5, 3, inf, None),\n",
+       " (5, 4, inf, None),\n",
+       " (5, 5, 0.0, 5),\n",
+       " (5, 6, 1.0, 6),\n",
+       " (5, 7, 2.0, 6),\n",
+       " (6, 0, inf, None),\n",
+       " (6, 1, inf, None),\n",
+       " (6, 2, inf, None),\n",
+       " (6, 3, inf, None),\n",
+       " (6, 4, inf, None),\n",
+       " (6, 5, inf, None),\n",
+       " (6, 6, 0.0, 6),\n",
+       " (6, 7, 1.0, 7),\n",
+       " (7, 0, inf, None),\n",
+       " (7, 1, inf, None),\n",
+       " (7, 2, inf, None),\n",
+       " (7, 3, inf, None),\n",
+       " (7, 4, inf, None),\n",
+       " (7, 5, inf, None),\n",
+       " (7, 6, inf, None),\n",
+       " (7, 7, 0.0, 7)]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_alt, out_alt_summary;\n",
+    "\n",
+    "SELECT madlib.graph_apsp(\n",
+    "                         'vertex_alt',                  -- Vertex 
table\n",
+    "                         'v_id',                        -- Vertex id 
column (NULL means use default naming)\n",
+    "                         'edge_alt',                    -- Edge table\n",
+    "                         'src=e_src, weight=e_weight',  -- Edge arguments 
(NULL means use default naming)\n",
+    "                         'out_alt');                    -- Output table 
of shortest paths\n",
+    "\n",
+    "SELECT * FROM out_alt ORDER BY e_src, dest;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 6. Grouping\n",
+    "Create a graph with 2 groups and find APSP for each group:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "21 rows affected.\n",
+      "1 rows affected.\n",
+      "22 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>src</th>\n",
+       "        <th>dest</th>\n",
+       "        <th>weight</th>\n",
+       "        <th>grp</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-20.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 1, 1.0, 0),\n",
+       " (0, 2, 1.0, 0),\n",
+       " (0, 4, 10.0, 0),\n",
+       " (1, 2, 2.0, 0),\n",
+       " (1, 3, 10.0, 0),\n",
+       " (2, 3, 1.0, 0),\n",
+       " (2, 5, 1.0, 0),\n",
+       " (2, 6, 3.0, 0),\n",
+       " (3, 0, 1.0, 0),\n",
+       " (4, 0, -2.0, 0),\n",
+       " (5, 6, 1.0, 0),\n",
+       " (6, 7, 1.0, 0),\n",
+       " (0, 1, 1.0, 1),\n",
+       " (0, 2, 1.0, 1),\n",
+       " (0, 4, 10.0, 1),\n",
+       " (1, 2, 2.0, 1),\n",
+       " (1, 3, 10.0, 1),\n",
+       " (2, 3, 1.0, 1),\n",
+       " (2, 5, 1.0, 1),\n",
+       " (3, 0, 1.0, 1),\n",
+       " (4, 0, -2.0, 1),\n",
+       " (4, 5, -20.0, 1)]"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS edge_gr;\n",
+    "\n",
+    "CREATE TABLE edge_gr AS\n",
+    "(\n",
+    "  SELECT *, 0 AS grp FROM edge\n",
+    "  UNION\n",
+    "  SELECT *, 1 AS grp FROM edge WHERE src < 6 AND dest < 6\n",
+    ");\n",
+    "\n",
+    "INSERT INTO edge_gr VALUES\n",
+    "(4,5,-20,1);\n",
+    "\n",
+    "SELECT * FROM edge_gr ORDER BY grp, src, dest;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 7. Find APSP for all groups"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "28 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>src</th>\n",
+       "        <th>dest</th>\n",
+       "        <th>weight</th>\n",
+       "        <th>parent</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
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+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
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+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
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+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
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+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
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+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
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+       "        <td>7</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
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+       "    </tr>\n",
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+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>14.0</td>\n",
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+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>6</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>7</td>\n",
+       "        <td>5.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-10.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>14.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-6.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 0, 0.0, 0),\n",
+       " (0, 0, 1, 1.0, 1),\n",
+       " (0, 0, 2, 1.0, 2),\n",
+       " (0, 0, 3, 2.0, 2),\n",
+       " (0, 0, 4, 10.0, 4),\n",
+       " (0, 0, 5, 2.0, 2),\n",
+       " (0, 0, 6, 3.0, 5),\n",
+       " (0, 0, 7, 4.0, 6),\n",
+       " (0, 1, 0, 4.0, 3),\n",
+       " (0, 1, 1, 0.0, 1),\n",
+       " (0, 1, 2, 2.0, 2),\n",
+       " (0, 1, 3, 3.0, 2),\n",
+       " (0, 1, 4, 14.0, 0),\n",
+       " (0, 1, 5, 3.0, 2),\n",
+       " (0, 1, 6, 4.0, 5),\n",
+       " (0, 1, 7, 5.0, 6),\n",
+       " (1, 0, 0, 0.0, 0),\n",
+       " (1, 0, 1, 1.0, 1),\n",
+       " (1, 0, 2, 1.0, 2),\n",
+       " (1, 0, 3, 2.0, 2),\n",
+       " (1, 0, 4, 10.0, 4),\n",
+       " (1, 0, 5, -10.0, 4),\n",
+       " (1, 1, 0, 4.0, 3),\n",
+       " (1, 1, 1, 0.0, 1),\n",
+       " (1, 1, 2, 2.0, 2),\n",
+       " (1, 1, 3, 3.0, 2),\n",
+       " (1, 1, 4, 14.0, 0),\n",
+       " (1, 1, 5, -6.0, 4)]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_gr, out_gr_summary;\n",
+    "\n",
+    "SELECT madlib.graph_apsp(\n",
+    "                         'vertex',      -- Vertex table\n",
+    "                         NULL,          -- Vertex id column (NULL means 
use default naming)\n",
+    "                         'edge_gr',     -- Edge table\n",
+    "                         NULL,          -- Edge arguments (NULL means use 
default naming)\n",
+    "                         'out_gr',      -- Output table of shortest 
paths\n",
+    "                         'grp'          -- Grouping columns\n",
+    ");\n",
+    "\n",
+    "SELECT * FROM out_gr WHERE src < 2 ORDER BY grp,src,dest;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 8. Find the path from vertex 0 to vertex 5 in every group"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "2 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>path</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>[0, 2, 5]</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>[0, 4, 5]</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, [0, 2, 5]), (1, [0, 4, 5])]"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_gr_path;\n",
+    "SELECT madlib.graph_apsp_get_path('out_gr',0,5,'out_gr_path');\n",
+    "SELECT * FROM out_gr_path ORDER BY grp;"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}

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