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228 lines
8.3 KiB
228 lines
8.3 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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! 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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! 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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! 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" content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; SunOS 5.7 sun4u) [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: HSFC</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> | <a href="ug_alg_reftree.html">Next</a> | <a href="ug_alg_rib.html">Previous</a></i></b></div>
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<h2>
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<a NAME="HSFC"></a>Hilbert Space Filling Curve (HSFC)</h2>
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The Inverse Hilbert Space-Filling Curve functions map a point in one, two or three dimensions
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into the interval [0,1]. The Hilbert functions that map [0, 1] to normal spatial
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coordinates are also provided. (The one-dimensional inverse Hilbert curve is defined here
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as the identity function, f(x)=x for all x.)
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<p>
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The HSFC partitioning algorithm seeks to divide [0,1] into P intervals each containing
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the same weight of objects associated to these intervals by their inverse Hilbert
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coordinates. N bins are created (where N > P) to partition [0,1]. The weights in
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each bin are summed across all processors.
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A greedy algorithm sums the bins (from left to right) placing a cut when the desired weight
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for current part interval is achieved.
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This process is repeated as needed to improve partitioning tolerance by
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a technique that maintains the same total number of bins but refines the bins previously
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containing a cut.
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<p>
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HSFC returns an warning if the final imbalance exceeds the user specified tolerance.
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<p>
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This code implements both the point assign and box assign functionality. The point
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assign determines an appropriate part (associated with a specific group of processors)
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for a new point. The box assign determines the list of processors
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whose associated subdomains intersect the given box. In order to
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use either of these routines, the user parameter KEEP_CUTS must be turned on.
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Both point assign and box assign now work for points or boxes anywhere in space even if
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they are exterior to the original bounding box. If a part is empty (due to the
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part being assigned zero work), it is not included in the list of parts
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returned by box assign. Note: the original box assign algorithm was not rigorous and
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may have missed parts. This version is both rigorous and fast.
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<p>
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The Zoltan implementation of HSFC has one parameter that can be modified
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by the <b><a href="ug_interface_init.html#Zoltan_Set_Param">Zoltan_Set_Param</a></b>
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function.
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<p>
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This partitioning algorithm is loosely based on the 2D & 3D Hilbert tables used in the Octree
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partitioner and on the BSFC partitioning implementation by Andrew C. Bauer, Department
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of Engineering, State University of New York at Buffalo, as his summer project at SNL
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in 2001. The box assign algorithm is loosely based on the papers by Lawder referenced both
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in the developers guide and the code itself. NOTE: This code can be trivially extended to
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any space filling curve by providing the tables implementing the curve's state transition
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diagram. The only dependance on the curve is through the tables and the box assign
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algorithm will work for all space filling curves (if we have their tables.)
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<p>
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Please refer to the Zoltan Developers Guide,
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<b><a href="../dev_html/dev_hsfc.html">Appendix: Hilbert Space Filling Curve (HSFC)</a></b>
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for more detailed information about these algorithms.
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<br>
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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>HSFC</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 NOSAVE> <i> KEEP_CUTS</i></td>
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<td>Information about cuts and bounding box is necessary
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if the application wants to add more objects to the decomposition via calls
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to <b><a href="ug_interface_augment.html#Zoltan_LB_Point_PP_Assign">Zoltan_LB_Point_PP_Assign</a></b>
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or to <b><a href="ug_interface_augment.html#Zoltan_LB_Box_PP_Assign">Zoltan_LB_Box_PP_Assign</a></b>.
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<br>0 = don't keep cuts; 1 = keep cuts.</td>
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</tr>
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<tr>
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<td VALIGN=TOP NOSAVE> <i> REDUCE_DIMENSIONS</i></td>
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<td>
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When a 3 dimensional geometry is almost flat, it may make more
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sense to treat it as a 2 dimensional geometry when applying the HSFC
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algorithm. (Coordinate values in the omitted direction are ignored for the purposes of partitioning.)
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If this parameter is set to <B>1</B>, a 3 dimensional
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geometry will be treated as 2 dimensional if is very flat,
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or 1 dimensional if it very thin. And a 2 dimensional geometry will
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be treated as 1 dimensional if it is very thin.
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Turning this parameter on removes the possibility that disconnected
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parts will appear on the surface of a flat 3 dimensional object.
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</td>
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</tr>
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<tr>
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<td VALIGN=TOP NOSAVE> <i> DEGENERATE_RATIO</i></td>
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<td>
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If the <B>REDUCE_DIMENSIONS</B> parameter is set, then this parameter
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determines when a geometry is considered to be flat.
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A bounding box which is oriented to the geometry is constructed, and
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the lengths of its sides are tested against a ratio of 1 : <B>DEGENERATE_RATIO</B>.
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</td>
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</tr>
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<tr>
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<td VALIGN=TOP><b>Default:</b></td>
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<td></td>
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</tr>
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<tr>
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<td></td>
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<td><i>KEEP_CUTS</i> = 0</td>
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</tr>
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<tr>
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<td></td>
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<td><i>REDUCE_DIMENSIONS</i> = 0</td>
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</tr>
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<tr>
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<td></td>
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<td><i>DEGENERATE_RATIO</i> = 10</td>
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</tr>
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<tr>
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<td VALIGN=TOP><b>Required Query Functions:</b></td>
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<td></td>
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</tr>
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<tr>
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<td></td>
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<td><b><a href="ug_query_lb.html#ZOLTAN_NUM_OBJ_FN">ZOLTAN_NUM_OBJ_FN</a></b></td>
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</tr>
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<tr>
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<td></td>
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<td><b><a href="ug_query_lb.html#ZOLTAN_OBJ_LIST_FN">ZOLTAN_OBJ_LIST_FN</a></b>
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</td>
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</tr>
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<tr>
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<td></td>
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<td>
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<b><a href="ug_query_lb.html#ZOLTAN_NUM_GEOM_FN">ZOLTAN_NUM_GEOM_FN</a></b>
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</td>
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</tr>
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<tr>
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<td></td>
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<td>
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<b><a href="ug_query_lb.html#ZOLTAN_GEOM_MULTI_FN">ZOLTAN_GEOM_MULTI_FN</a></b>
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or <b><a href="ug_query_lb.html#ZOLTAN_GEOM_FN">ZOLTAN_GEOM_FN</a></b>
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</td>
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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> |
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<a href="ug_alg_reftree.html">Next: Refinement Tree Partitioning</a>
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| <a href="ug_alg_rib.html">Previous: Recursive Inertial Bisection</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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