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127 lines
5.5 KiB
127 lines
5.5 KiB
<!-------- @HEADER
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!
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! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!
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! Zoltan Toolkit for Load-balancing, Partitioning, Ordering and Coloring
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! Copyright 2012 Sandia Corporation
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! Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
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! the U.S. Government retains certain rights in this software.
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!
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! Redistribution and use in source and binary forms, with or without
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! modification, are permitted provided that the following conditions are
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! met:
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!
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! 1. Redistributions of source code must retain the above copyright
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! notice, this list of conditions and the following disclaimer.
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! 2. Redistributions in binary form must reproduce the above copyright
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! notice, this list of conditions and the following disclaimer in the
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! documentation and/or other materials provided with the distribution.
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!
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! 3. Neither the name of the Corporation nor the names of the
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! contributors may be used to endorse or promote products derived from
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! this software without specific prior written permission.
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! THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
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! Questions? Contact Karen Devine kddevin@sandia.gov
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! Erik Boman egboman@sandia.gov
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! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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! @HEADER
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------->
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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<html>
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<head>
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<meta http-equiv="Content-Type"
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content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR"
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content="Mozilla/4.76 [en] (X11; U; Linux 2.4.2-2smp i686) [Netscape]">
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<meta name="sandia.approval_type" content="formal">
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<meta name="sandia.approved" content="SAND2007-4748W">
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<meta name="author" content="Zoltan PI">
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<title>Zoltan User's Guide: Graph vs. Hypergraph Partitioning</title>
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</head>
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<body bgcolor="#ffffff">
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<div align="right"><b><i><a href="ug.html">Zoltan User's Guide</a> |
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<a href="ug_alg_parmetis.html"> Next</a> |
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<a href="ug_alg_graph.html">Previous</a>
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</i>
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</b></div>
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<h2>
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<a name="Graph vs Hypergraph Partitioning">
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</a>Graph vs Hypergraph Partitioning</h2>
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Graph partitioning has proven quite useful in scientific computing.
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<a href="ug_alg_hypergraph.html">Hypergraph partitioning</a>
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is a more recent improvement
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that uses a hypergraph model, which is
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often a more accurate model than the graph model for scientific computing.
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(Hypergraphs contain hyperedges which connect two <i>or more</i>
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vertices.)
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See <a href="ug_refs.html#catalyurek99">[Catalyurek & Aykanat]</a> and
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<a href="ug_refs.html#hendrickson-kolda">[Hendrickson & Kolda]</a>
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for further details.
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You do not need to understand the underlying models
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to use graph or hypergraph partitioning for load-balancing
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in Zoltan. The basic trade-offs are:
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<ul>
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<li> Hypergraph partitioning usually produces partitions (assignments)
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of higher quality than graph partitioning, which may reduce
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communication time in parallel applications (up to 30-40%
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reduction has been reported). However, hypergraph
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partitioning takes longer time to compute. </li>
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<li> The graph model is restricted to symmetric data dependencies.
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If you have a non-symmetric problem, we recommend hypergraph
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partitioning. </li>
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</ul>
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<h3>Migrating from ParMetis to PHG in Zoltan</h3>
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If you already use Zoltan for graph partitioning (via ParMetis),
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there are three ways to switch to the Zoltan-PHG hypergraph partitioner:
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<ol>
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<li>The quick and easy way: Just change the <a href="ug_alg.html#LB_METHOD">
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LB_METHOD</a> to "Hypergraph".
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Zoltan will then use the graph query functions (presumably
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already implemented) to construct a hypergraph model, which
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is similar to but not equivalent to the graph.
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<li>The proper way: Change the LB_METHOD, but also implement and
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register the <a href="ug_query_lb.html#ZOLTAN_HG_SIZE_CS_FN">
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hypergraph query functions</a>
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required by Zoltan. These may give a more accurate representation
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of data dependencies (and communication requirements) for your
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application.
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<li>If you really want graph (not hypergraph) partitioning:
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Just change the <a href="ug_alg.html#LB_METHOD">
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LB_METHOD</a> to "Graph".
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Zoltan will then use PHG as a graph partitioner, which is slower than
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ParMetis but often produces better partitions (lower cuts).
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</ol>
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Technical note: A hypergraph is constructed from the graph as follows:
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The vertices are the same in the hypergraph as in the graph. For each vertex
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<i>v</i>, create a hyperedge that consists of all neighbors in the graph
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and <i>v </i> itself.
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<hr width="100%">[<a href="ug.html">Table of Contents</a> |
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<a href="ug_alg_parmetis.html"> Next: ParMETIS</a> |
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<a href="ug_alg_graph.html">Previous:
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Graph Partitioning</a> | <a href="https://www.sandia.gov/general/privacy-security/index.html">Privacy and Security</a>]
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</body>
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</html>
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