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<title>Zoltan User's Guide: ParMETIS Interface</title>
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<h2>
<a name="ParMETIS"></a>ParMETIS - Parallel Graph Partitioning</h2>
<a href="https://www-users.cs.umn.edu/%7Ekarypis/metis/parmetis/">ParMETIS</a>
is a parallel library for graph partitioning (for static load
balancing)
and repartitioning (for dynamic load balancing) developed at the
University
of Minnesota by Karypis, Schloegel and Kumar [<a
href="ug_refs.html#parmetis">Karypis
and Kumar</a>]. Note that ParMetis must be obtained separately and has a different license than Zoltan (see page 31 of <a
href="https://glaros.dtc.umn.edu/gkhome/fetch/sw/parmetis/manual.pdf">
this manual</a>). ParMETIS is strictly speaking not a method but
rather a collection of methods. In the Zoltan context, ParMETIS is a
method
with many sub-methods. Zoltan provides an interface to all the ParMETIS
(sub-)methods. The user selects which ParMETIS method to use
through
the parameter PARMETIS_METHOD. Most of the ParMETIS methods are based
on
either multilevel Kernighan-Lin partitioning or a diffusion algorithm.
The names of the ParMETIS methods used by Zoltan are identical to those
in the ParMETIS library. For further information about the various <a
href="https://www-users.cs.umn.edu/%7Ekarypis/metis/parmetis/">ParMETIS</a>
methods and parameters, please consult the <a
href="https://www-users.cs.umn.edu/%7Ekarypis/metis/parmetis/">ParMETIS</a>
User's Guide.
<p>Graph partitioning is a useful abstraction for load balancing. The
main
idea is to represent the computational application as a weighted graph.
The nodes or vertices in the graph correspond to objects in
Zoltan.
Each object may have a weight that normally represents the amount of
computation.
The edges or arcs in the graph usually correspond to communication
costs.
In graph partitioning, the problem is to find a partition of the
graph
(that is, each vertex is assigned to one out of <i>k</i>
possible
sets called parts) that minimizes the cut size (weight) subject to
the parts having approximately equal size (weight). In
repartitioning,
it is assumed that a partition already exists. The problem is to
find
a good partition that is also "similar" in some sense to the
existing
partition. This keeps the migration cost low. All the problems
described
above are NP-hard so no efficient exact algorithm is known, but
heuristics work well in practice.<br>
</p>
<p>We give only a brief summary of the various ParMETIS methods here;
for
more details see the <a
href="https://www-users.cs.umn.edu/%7Ekarypis/metis/parmetis/">ParMETIS</a>
documentation. The methods fall into three categories:
</p>
<ol>
<li>
Part* - Perform graph partitioning without consideration of the initial
distribution. (LB_APPROACH=partition)<br>
</li>
<li>
AdaptiveRepart - Incremental
algorithms with small migration cost. (LB_APPROACH=repartition)</li>
<li>
Refine* - Refines a given partition (balance). Can be applied
multiple times to reduce the communication cost (cut weight) if
desired. (LB_APPROACH=refine)</li>
</ol>
As a rule of thumb, use one of the Part* methods if you have a poor
initial
balance and you are willing to spend some time doing migration. One
such
case is static load balancing; that is, you need to balance only once.
Use AdaptiveRepart or the Repart* methods when you have a reasonably
good
load balance that you wish to update incrementally. These methods are
well
suited for dynamic load balancing (for example, adaptive
mesh
refinement). A reasonable strategy is to call PartKway once to obtain a
good initial balance and later update this balance using
AdaptiveRepart.
<p>
Zoltan supports the multiconstraint partitioning
feature of ParMETIS through multiple object weights (see <i><a
href="ug_param.html#General_Parameters">OBJ_WEIGHT_DIM</a></i>).
</p>
<p>The graph given to Zoltan/ParMETIS must be symmetric. Any self edges
(loops) will be ignored. Multiple edges between a pair of vertices is
not allowed. All weights must be non-negative. The graph does not have to
be connected.
</p>
<p>Zoltan is currently compatible with ParMETIS version 3.1 and 4.0.x.
The ParMETIS source code can be obtained from
the <a href="https://glaros.dtc.umn.edu/gkhome/views/metis/parmetis">
ParMETIS home page</a>. ParMETIS has a separate license:
<i>'PARMETIS can be freely used for educational and research purposes by non-profit institutions and US government agencies only. Other organizations are allowed to
use PARMETIS only for evaluation purposes, and any further uses will require prior approval from <a href="https://www.license.umn.edu/Products/ParMETIS---Mesh-Graph-Partitioning-Algorithm__Z09041.aspx">the technology transfer office at the University of Minnesota</a>'
</i> <br>
If you do not wish to install ParMETIS, it
is possible to compile Zoltan without any references to ParMETIS;
(when you 'make' Zoltan, comment out the PARMETIS_LIBPATH variable in
the
configuration file <i><a href="ug_usage.html#Building%20the%20Library">Utilities/Config/Config.<platform></a></i>).
</p>
<br>
<table nosave="" width="100%">
<tbody>
<tr>
<td valign="top"><b>Value of LB_METHOD:</b></td>
<td><b>GRAPH</b></td>
</tr>
<tr>
<td valign="top"><b>Value of GRAPH_PACKAGE:</b></td>
<td><b>Parmetis</b></td>
</tr>
<tr>
<td><b>Parameters:</b></td>
<td><br>
</td>
</tr>
<tr>
<td valign="top"><i> LB_APPROACH<br>
</i></td>
<td>The load balancing approach:. <br>
<i>PARTITION</i> - partition from scratch, not taking
the current data distribution into account<br>
<i>REPARTITION</i> - partition but try to stay close to the
current partition/distribution
<br>
<i>REFINE</i> - refine the current partition/distribution;
assumes only small changes
</td>
</tr>
<tr>
<td valign="top"><i> PARMETIS_METHOD</i></td>
<td>The specific ParMETIS method to be used (see below).
Note: See also <a href="ug_alg.html#LB_APPROACH">LB_APPROACH</a>,
which is a simpler way to specify the overall load balance approach.
Only use <i>PARMETIS_METHOD</i> if you really need a specific
implementation.<br>
<i>PartKway</i> - multilevel Kernighan-Lin partitioning
<br>
<i>PartGeom</i> - space filling curves (coordinate based)
<br>
<i>PartGeomKway</i> - hybrid method based on PartKway and
PartGeom
(needs both graph data and coordinates)
<br>
<i>AdaptiveRepart - </i>adaptive repartitioning (only in
ParMETIS 3.0
and higher)
<br>
<i>RefineKway</i> - refine the current partition (balance)</td>
</tr>
<tr>
<td><br>
</td>
<td>The method names are case insensitive.</td>
</tr>
<tr>
<td valign="top"> <i>PARMETIS_OUTPUT_LEVEL</i></td>
<td>Amount of output the load-balancing algorithm should
produce.
<br>
0 = no output, 1 = print timing info. Turning on more bits displays
more information (for example, 3=1+2, 5=1+4, 7=1+2+4).</td>
</tr>
<tr>
<td> <i>PARMETIS_COARSE_ALG</i></td>
<td>Coarse algorithm for PartKway. 1 = serial, 2 = parallel.
(ParMETIS
2 only)</td>
</tr>
<tr>
<td> <i>PARMETIS_SEED</i></td>
<td>Random seed for ParMETIS.</td>
</tr>
<tr nosave="" valign="top">
<td> <i>PARMETIS_ITR</i></td>
<td nosave="">Ratio of interprocessor communication time to
redistribution
time. A high value will emphasize reducing the edge cut, while a small
value will try to keep the change in the new partition (distribution)
small.
This parameter is used only by AdaptiveRepart. A value of between 100
and
1000 is good for most problems.</td>
</tr>
<tr nosave="" valign="top">
<td> <i>CHECK_GRAPH</i></td>
<td nosave="">Level of error checking for graph input: 0 = no
checking, 1
= on-processor checking, 2 = full checking. (CHECK_GRAPH==2 is very
slow
and should be used only during debugging).</td>
</tr>
<tr nosave="" valign="top">
<td> <i>SCATTER_GRAPH</i></td>
<td nosave="">Scatter graph data by distributing contiguous
chunks of objects
(vertices) of roughly equal size to each processor before calling the
partitioner.
0 = don't scatter;
1 = scatter only if all objects are on a single processor;
2 = scatter if at least one processor owns no objects;
3 = always scatter. </td>
</tr>
<tr nosave="" valign="top">
<td> <i>GRAPH_SYMMETRIZE</i></td>
<td nosave="">How to symmetrize the graph:
NONE = graph is symmetric and no symmetrization is needed <br/>
TRANSPOSE = if M is adjacency matrix of the input graph, output will be the graph representation of M+M<sup>T</sup> <br/>
BIPARTITE = graph is symmetrized in a bipartite way : [[ 0 M ][M<sup>t</sup> 0]]
</td>
</tr>
<tr nosave="" valign="top">
<td> <i>GRAPH_SYM_WEIGHT</i></td>
<td nosave="">How edge weights are handled during symmetrization:
ADD = weights of each arc are added <br/>
MAX = only the heaviest arc weight is kept <br/>
<p>See more informations about graph build options on this <a href="ug_graph_build.html">page</a></p>
<!-- ERROR = fail if complementary arcs don't have the same weight. -->
</td>
</tr>
<!-- <tr nosave="" valign="top"> -->
<!-- <td> <i>GRAPH_BIPARTITE_TYPE</i></td> -->
<!-- <td nosave=""> In the case of a bipartite symmetrization, -->
<!-- NONE = graph is symmetric and no symmetrization is needed <br/> -->
<!-- TRANSPOSE = if M is adjacency matrix of the input graph, output will be the graph representation of M+M<sup>T</sup> <br/> -->
<!-- BIPARTITE = graph is symmetrized in a bipartite way : [[ 0 M ][M<sup>t</sup> 0]] -->
<!-- </td> -->
<!-- </tr> -->
<tr>
<td valign="top"><b>Default values:</b></td>
<td><br>
</td>
</tr>
<tr>
<td><br>
</td>
<td><i>LB_APPROACH</i> = Repartition</td>
</tr>
<tr>
<td><br>
</td>
<td><i>PARMETIS_METHOD</i> = AdaptiveRepart</td>
</tr>
<tr>
<td><br>
</td>
<td><i>PARMETIS_OUTPUT_LEVEL</i> = 0</td>
</tr>
<tr>
<td><br>
</td>
<td><i>PARMETIS_COARSE_ALG </i>= 2</td>
</tr>
<tr>
<td><br>
</td>
<td><i>PARMETIS_SEED </i>= 15</td>
</tr>
<tr>
<td><br>
</td>
<td><i>PARMETIS_ITR </i>= 100</td>
</tr>
<tr>
<td><br>
</td>
<td><i>USE_OBJ_SIZE </i>= 1</td>
</tr>
<tr>
<td><br>
</td>
<td><i>CHECK_GRAPH</i> = 1</td>
</tr>
<tr>
<td><br>
</td>
<td><i>SCATTER_GRAPH </i>= 1</td>
</tr>
<tr>
<td><br>
</td>
<td><i>GRAPH_SYMMETRIZE </i>= NONE</td>
</tr>
<tr>
<td><br>
</td>
<td><i>GRAPH_SYM_WEIGHT </i>= ADD</td>
</tr>
<tr>
<td valign="top"><b>Required Query Functions:</b></td>
<td><br>
</td>
</tr>
<tr>
<td>For all submethods:</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_NUM_OBJ_FN">ZOLTAN_NUM_OBJ_FN</a></b></td>
</tr>
<tr>
<td><br>
</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_OBJ_LIST_FN">ZOLTAN_OBJ_LIST_FN</a></b>
</td>
</tr>
<tr>
<td>Only PartGeom & PartGeomKway:</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_NUM_GEOM_FN">ZOLTAN_NUM_GEOM_FN</a></b></td>
</tr>
<tr>
<td><br>
</td>
<td>
<b><a href="ug_query_lb.html#ZOLTAN_GEOM_MULTI_FN">ZOLTAN_GEOM_MULTI_FN</a></b>
or <b><a href="ug_query_lb.html#ZOLTAN_GEOM_FN">ZOLTAN_GEOM_FN</a></b>
</td>
</tr>
<tr nosave="" valign="top">
<td>All but PartGeom:</td>
<td nosave="">
<b><a href="ug_query_lb.html#ZOLTAN_NUM_EDGES_MULTI_FN">ZOLTAN_NUM_EDGES_MULTI_FN</a></b>
or
<b><a href="ug_query_lb.html#ZOLTAN_NUM_EDGES_FN">ZOLTAN_NUM_EDGES_FN</a></b>
<br>
<b><a href="ug_query_lb.html#ZOLTAN_EDGE_LIST_MULTI_FN">ZOLTAN_EDGE_LIST_MULTI_FN</a></b>
or
<b><a href="ug_query_lb.html#ZOLTAN_EDGE_LIST_FN">ZOLTAN_EDGE_LIST_FN</a></b>
</td>
</tr>
<tr>
<td valign="top"><b>Optional Query Functions:</b></td>
<td><br>
</td>
</tr>
<tr>
<td><br>
</td>
<td>
<b><a href="ug_query_mig.html#ZOLTAN_OBJ_SIZE_MULTI_FN">ZOLTAN_OBJ_SIZE_MULTI_FN</a></b>
or
<b><a href="ug_query_mig.html#ZOLTAN_OBJ_SIZE_FN">ZOLTAN_OBJ_SIZE_FN</a></b> for <i>PARMETIS_METHOD</i>=<i>AdaptiveRepart</i>
</td>
</tr>
<tr>
<td><br>
</td>
<td>
<b><a href="ug_query_lb.html#ZOLTAN_PART_MULTI_FN">ZOLTAN_PART_MULTI_FN</a></b>
or
<b><a href="ug_query_lb.html#ZOLTAN_PART_FN">ZOLTAN_PART_FN</a></b> for part remapping in ParMETIS.
</td>
</tr>
</tbody>
</table>
</p>
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