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156 lines
6.4 KiB
156 lines
6.4 KiB
2 years ago
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<!-------- @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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!
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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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!
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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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!
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! THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
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! EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
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! CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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! EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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! PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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! PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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! LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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! NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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! SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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!
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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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! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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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" content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" 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: Hypergraph Algorithms</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_phg.html">Next</a> | <a href="ug_alg_reftree.html">Previous</a></i></b></div>
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<h2>
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<a NAME="Hypergraph"></a>Hypergraph partitioning</h2>
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Hypergraph partitioning is a useful partitioning and
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load balancing method when connectivity data is available. It can be
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viewed as a more sophisticated alternative to
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the traditional graph partitioning.
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<p>A hypergraph consists of vertices and hyperedges. A hyperedge
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connects
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one or more vertices.
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A graph can be cast as a hypergraph in one of two ways: either every
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pair of neighboring vertices form a hyperedge, or a vertex and all
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its neighbors form a hyperedge.
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The hypergraph model is well
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suited to parallel computing, where vertices correspond to data objects
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and hyperedges represent the communication requirements. The basic
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partitioning problem is to partition the vertices into <i>k</i>
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approximately equal sets such that the number of cut hyperedges is
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minimized. Most partitioners (including Zoltan-PHG) allows a more
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general
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model where both vertices and hyperedges can be assigned weights.
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It has been
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shown that the hypergraph model gives a more accurate representation
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of communication cost (volume) than the graph model. In particular,
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for sparse matrix-vector multiplication, the hypergraph model
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<strong>exactly</strong> represents communication volume. Sparse
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matrices can be partitioned either along rows or columns;
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in the row-net model the columns are vertices and each row corresponds
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to an hyperedge, while in the column-net model the roles of vertices
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and hyperedges are reversed. </p>
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<p>Zoltan contains a native parallel hypergraph partitioner, called PHG
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(Parallel HyperGraph partitioner). In addition, Zoltan provides
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access to <a href="https://bmi.osu.edu/%7Eumit/software.htm">PaToH</a>,
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a serial hypergraph partitioner.
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Note that PaToH is not part of Zoltan and should be obtained
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separately from the <a href="https://bmi.osu.edu/%7Eumit/software.htm">
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PaToH web site</a>.
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Zoltan-PHG is a fully parallel multilevel hypergraph partitioner. For
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further technical description, see <a
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href="ug_refs.html#hypergraph-ipdps06">[Devine et al, 2006]</a>.<br>
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</p>
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<p>
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A new feature available in Zoltan 3.0 is the ability to assign selected
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objects (vertices) to a particular part ("fixed vertices").
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When objects are fixed,
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Zoltan will not migrate them out of the user assigned part.
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See the descriptions of the
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<i><a href="ug_query_lb.html#ZOLTAN_NUM_FIXED_OBJ_FN">ZOLTAN_NUM_FIXED_OBJ_FN</a></i>
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and
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<i><a href="ug_query_lb.html#ZOLTAN_FIXED_OBJ_LIST_FN">ZOLTAN_FIXED_OBJ_LIST_FN</a></i>
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query functions for a discussion of how you can define these two
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functions to fix objects to parts. Both PHG and PaToH support this
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feature.
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<p>
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For applications that already use Zoltan to do graph partitioning,
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it is easy to upgrade to hypergraph partitioning. For many applications,
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the hypergraph model is superior to the graph model, but in some cases
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the graph model should be preferred. PHG can also be used as a pure
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graph partitioner. See the section
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<a href="ug_graph_vs_hg.html">graph vs. hypergraph</a> partitioning
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for further details. </p>
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<br>
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<table WIDTH="100%" NOSAVE >
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<tr>
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<td VALIGN=TOP><b>Method String:</b></td>
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<td><b>HYPERGRAPH</b></td>
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</tr>
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<tr>
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<td><b>Parameters:</b></td>
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<td></td>
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</tr>
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<tr>
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<td VALIGN=TOP><i> HYPERGRAPH_PACKAGE</i></td>
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<td>The software package to use in partitioning the hypergraph.
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<br><i><a href=ug_alg_phg.html>PHG (Zoltan, the default)</a></i>
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<br><i><a href=ug_alg_patoh.html>PATOH</a></i>
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</tr>
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</table>
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<p>
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<hr WIDTH="100%">[<a href="ug.html">Table of Contents</a> | <a href="ug_alg_phg.html">Next:
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PHG</a> | <a href="ug_alg_reftree.html">Previous:
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Refinement Tree 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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