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177 lines
9.0 KiB
177 lines
9.0 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/4.7 [en] (X11; U; SunOS 5.6 sun4m) [Netscape]">
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<meta name="sandia.approved" content="SAND99-1376">
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<meta name="author" content="karen devine, kddevin@sandia.gov">
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<title> Zoltan Developer's Guide: ParMETIS/Jostle</title>
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</head>
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<body bgcolor="#FFFFFF">
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<div align=right><b><i><a href="dev.html">Zoltan Developer's Guide</a>
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| <a href="dev_phg.html">Next</a> | <a href="dev_rib.html">Previous</a></i></b></div>
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<h2>
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Appendix: <a href="https://www-users.cs.umn.edu/~karypis/metis/parmetis/">ParMETIS</a>
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and <a href="https://www.gre.ac.uk/jostle">Jostle</a></h2>
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<h3>
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Overview of structure (algorithm)</h3>
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This part of Zoltan provides an interface to various graph-based load-balancing
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algorithms. Currently two libraries are supported: <a href="../ug_html/ug_alg_parmetis.html">ParMETIS
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</a>and
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<a href="../ug_html/ug_alg_jostle.html">Jostle.</a>
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Each of these libraries contain several algorithms.
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<h4>
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Interface algorithm</h4>
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The structure of the code is as follows: Each package
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(<a href="https://www-users.cs.umn.edu/~karypis/metis/parmetis/">ParMETIS</a>,
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<a href="https://www.gre.ac.uk/jostle">Jostle</a>)
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has its own wrapper routine that performs initialization and sets parameters.
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The main routine is <b>Zoltan_ParMetis_Jostle,</b> which constructs an appropriate
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graph data structure using Zoltan's query functions. After the graph structure
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has been constructed, the appropriate library is called and the import/export
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list is created and returned.
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<p>Please note that <a href="https://www-users.cs.umn.edu/~karypis/metis/parmetis/">ParMETIS</a>
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and <a href="https://www.gre.ac.uk/jostle">Jostle</a> are not integral parts
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of Zoltan. These libraries must be obtained and installed separately.
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(<a href="https://www-users.cs.umn.edu/~karypis/metis/parmetis/">ParMETIS</a>
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may be bundled with Zoltan, but it is an independent package developed
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at Univ. of Minnesota.) Zoltan merely provides an interface to these libraries.
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<p>The most complex task in the interface code is the construction of the
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graph data structure. This structure is described in the next section.
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The routine uses the Zoltan query functions to get a list of objects and
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edges on each processor. Each object has a unique global ID which is mapped
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into a unique (global) number between 1 and <i>n</i>, where <i>n</i> is
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the total number of objects. The construction of the local (on-processor)
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part of the graph is straightforward. When an edge goes between objects
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that reside on different processors, global communication is required.
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We use Zoltan's unstructured communication library for this. A hash function
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(<a href="dev_services_hash.html"><b>Zoltan_Hash</b></a>) is used to efficiently map global IDs to integers.
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The graph construction algorithm has parallel complexity
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<i>O(max<sub>j</sub> {n<sub>j</sub>+m<sub>j</sub>+p})</i>, where
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<i>n<sub>j</sub></i> is the number of objects on processor j,
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<i>m<sub>j</sub></i> is the number of edges on processor j, and
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<i>p</i> is the number of processors.
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<p>One other feature of the interface code should be mentioned. While
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Zoltan allows objects and edges to have real (float) weights, both ParMETIS and Jostle
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currently require integer weights. Therefore, Zoltan first checks if the
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object weights are integers. If not, the weights are automatically scaled
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and rounded to integers. The scaling is performed such that the weights
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become large integers, subject to the constraint that the sum of (any component
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of) the weights is less than a large constant MAX_WGT_SUM < INT_MAX.
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The scaled weights are rounded up to the nearest integer to ensure that
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nonzero weights never become zero.
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Note that for multidimensional weights, each weight component is scaled independently.
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(The source code is written such that this scaling is simple to change.)
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<p>Currently Zoltan constructs and discards the entire graph structure
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every time a graph-based method (ParMETIS or Jostle) is called. Incremental
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update of the graph structure may be supported in the future.
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<p>The graph construction code in <b>Zoltan_ParMetis_Jostle </b>can also be
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used to interface with other graph-based algorithms.
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<h4>
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Algorithms used in ParMETIS and Jostle libraries</h4>
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There are two main types of algorithms used in ParMETIS and Jostle. The
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first is multilevel graph partitioning. The main idea is to take a large
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graph and construct a sequence of smaller and simpler graphs that
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in some sense approximate the original graph. When the graph is sufficiently
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small it is partitioned using some other method. This smallest graph and
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the corresponding partition is then propagated back through all the levels
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to the original graph. A popular local refinement strategy known as Kernighan-Lin
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is employed at some or every level.
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<p>The second main strategy is diffusion. This method assumes that an initial
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partition (balance) is given, and load balance is achieved by repeatedly
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moving objects (nodes) from parts (processors) that have too heavy
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load to neighboring parts (processors) with too small load.
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<p>For further details about the algorithms in a specific library, please
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refer to the documentation that is distributed with that library.
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<h3>
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Data structures</h3>
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We use the ParMETIS parallel graph structure. This is implemented using
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5 arrays:
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<ol>
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<li>
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<i>vtxdist</i>: gives the distribution of the objects (vertices) to processors</li>
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<li>
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<i>xadj</i>: indices (pointers) to the <i>adjncy</i> array</li>
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<li>
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<i>adjncy</i>: neighbor lists</li>
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<li>
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<i>adjwgt</i>: edge weights</li>
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<li>
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<i>vwgt</i>: vertex (object) weights</li>
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</ol>
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The <i>vtxdist</i> array is duplicated on all processors, while the other
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arrays are local.
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<br>For more details, see the ParMETIS User's Guide.
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<h3>
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Parameters</h3>
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Zoltan supports the most common parameters in ParMETIS and Jostle. These
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parameters are parsed in the package-specific wrapper routine (<b>Zoltan_ParMetis</b>
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or <b>Zoltan_Jostle</b>) and later passed on to the desired library via <b>Zoltan_ParMetis_Jostle</b>.
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<p>In addition, Zoltan has one graph parameter of its own: <a href="../ug_html/ug_alg_parmetis.html">CHECK_GRAPH</a>.
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This parameter is set in <b>Zoltan_ParMetis_Jostle</b> and specifies the amount
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of verification that is performed on the constructed graph. For example, it
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is required that the graph is symmetric and that the weights are non-negative.
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<h3>
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Main routine</h3>
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The main routine is <b>Zoltan_ParMetis_Jostle</b> but it should always be accessed
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through either <b>Zoltan_ParMetis</b> or <b>Zoltan_Jostle</b>.
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<p>
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<hr WIDTH="100%">
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<br>[<a href="dev.html">Table of Contents</a> | <a href="dev_phg.html">Next:
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Hypergraph Partitioning</a> | <a href="dev_rib.html">Previous:
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Recursive Inertial Bisection (RIB)</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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