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<title>Zoltan User's Guide: Hypergraph Partitioning</title>
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<h2 =""><a name="PHG"></a>PHG - Parallel Hypergraph and Graph Partitioning with
Zoltan</h2>
This is the built-in parallel hypergraph partitioner in Zoltan.
<p>
<table nosave="" width="100%">
<tbody>
<tr>
<td valign="top"><b>Value of LB_METHOD:</b></td>
<td><b>HYPERGRAPH</b> (for <a href="ug_alg_hypergraph.html">hypergraph</a> partitioning) or <br>
<b>GRAPH</b> (for <a href="ug_alg_graph.html">graph</a> partitioning)
</td>
</tr>
<tr>
<td valign="top"><b>Value of HYPERGRAPH_PACKAGE:</b></td>
<td><b>PHG</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>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
<br>
<i>PARTITION</i> - partition from scratch, not taking
the current data distribution into account<br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <span
style="font-style: italic;">PHG_REPART_MULTIPLIER</span><br>
</td>
<td style="vertical-align: top;"> For repartitioning, this
parameter determines the trade-off between application communication
(as represented by cut edges) and data migration related to
rebalancing. PHG attempts to minimize the function
(PHG_REPART_MULTIPLIER* edge_cut + migration volume). The migration
volume is measured using the <a href="ug_query_mig.html#ZOLTAN_OBJ_SIZE_MULTI_FN">ZOLTAN_OBJ_SIZE_MULTI_FN</a> or <a href="ug_query_mig.html#ZOLTAN_OBJ_SIZE_FN">ZOLTAN_OBJ_SIZE_FN</a> query functions. Make sure the
units for edges and object sizes are the same.<br>
Simply put, to emphasize communication within the application, use a
large value for PHG_REPART_MULTIPLIER. Typically this should be
proportional to the number of iterations between load-balancing calls. </td>
</tr>
<tr>
<td valign="top"><i> PHG_MULTILEVEL<br>
</i></td>
<td>This parameter specifies whether a multilevel method
should be used (1) or not (0). Multilevel methods produce higher quality but
require more execution time and memory.
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <a
name="PHG_EDGE_WEIGHT_OPERATION"></a><span style="font-style: italic;">PHG_EDGE_WEIGHT_OPERATION</span>
</td>
<td style="vertical-align: top;">Operation to be applied to edge
weights supplied by different processes for the same hyperedge:<br>
<i>ADD</i> - the hyperedge weight will be the sum of the supplied
weights<br>
<i>MAX</i> - the hyperedge weight will be the maximum of the
supplied weights<br>
<i>ERROR</i> - if the hyperedge weights are not equal, Zoltan
will flag an error, otherwise the hyperedge weight will be the value
returned by the processes<br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <span
style="font-style: italic;">ADD_OBJ_WEIGHT</span><br>
</td>
<td style="vertical-align: top;"> Add another object (vertex)
weight. Currently multi-weight partitioning is not supported, but this
parameter may also be used for implicit vertex weights. Valid values
are: <br>
<i>NONE</i> <br>
<i>UNIT</i> or <i>VERTICES</i> (each vertex has weight 1.0) <br>
<i>PINS</i> or <i>NONZEROS</i> or <i>vertex degree</i> (vertex
weight equals number of hyperedges containing it, i.e., the degree)<br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <span
style="font-style: italic;">PHG_CUT_OBJECTIVE</span><br>
</td>
<td style="vertical-align: top;"> Selects the partitioning
objective, <i>CONNECTIVITY</i> or <i>HYPEREDGES</i>. While hyperedges
simply counts the number of hyperedges cut, the connectivity metric
weights each cut edge by the number of participating parts minus one
(aka the λ-1 cut metric). The connectivity metric better represents
communication volume for most applications. The hyperedge metric is
useful for certain applications, e.g., minimizing matrix border size in
block matrix decompositions. <br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"><span style="font-style: italic;">
PHG_OUTPUT_LEVEL</span><br>
</td>
<td style="vertical-align: top;">Level of verbosity; 0 is silent.<br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <span
style="font-style: italic;">CHECK_HYPERGRAPH</span><br>
</td>
<td style="vertical-align: top;">Check that the query functions
return valid input data; 0 or 1. (This slows performance; intended for
debugging.)<br>
</td>
</tr>
<tr>
<td valign="top"><i> PHG_COARSENING_METHOD</i></td>
<td>Low-level parameter: The method to use in the matching/coarsening phase:<br>
<span style="font-style: italic;">AGG</span> - agglomerative inner product
matching (a.k.a. agglomerative heavy connectivity matching); gives high quality.<br>
<span style="font-style: italic;">IPM</span> - inner product
matching (a.k.a. heavy connectivity matching); gives high quality.<br>
<span style="font-style: italic;">L-IPM </span>- local IPM
on each processor. Faster but usually gives poorer quality. <br>
<span style="font-style: italic;">A-IPM</span> - alternate
between IPM and L-IPM. (A compromise between speed and quality.)<br>
<span style="font-style: italic;">none - </span>no
coarsening<i><br>
</i></td>
</tr>
<tr>
<td valign="top"> <i>PHG_COARSEPARTITION_METHOD</i></td>
<td>Low-level parameter: Method to partition the coarsest (smallest) hypergraph;
typically done in serial:<br>
<span style="font-style: italic;">RANDOM</span> - random<br>
<span style="font-style: italic;">LINEAR</span> - linear
assignment of the vertices (ordered by the user query function)<br>
<span style="font-style: italic;">GREEDY</span> - greedy method
based on minimizing cuts<br>
<span style="font-style: italic;">AUTO</span> -
automatically select from the above methods (in parallel, the processes
will do different methods)<br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <span
style="font-style: italic;">PHG_REFINEMENT_METHOD</span><br>
</td>
<td style="vertical-align: top;">Low-level parameter: Refinement algorithm:<br>
<span style="font-style: italic;">FM</span> - approximate
Fiduccia-Mattheyses (FM)<br>
<span style="font-style: italic;">NO</span> - no refinement<br>
</td>
</tr>
<tr>
<td valign=top> <i>PHG_REFINEMENT_QUALITY</i></td>
<td>Low-level parameter: Knob to control the trade-off between run time and quality. 1
is the recommended (default) setting, >1 gives more refinement
(higher quality partitions but longer run time), while <1 gives less
refinement (and
poorer quality).<br>
</td>
</tr>
<tr>
<td style="vertical-align: top;"> <span
style="font-style: italic;">PHG_RANDOMIZE_INPUT</span><br>
</td>
<td style="vertical-align: top;">Low-level parameter: Randomize layout of vertices and
hyperedges in internal parallel 2D layout? <br>
Setting this parameter to 1 often reduces Zoltan-PHG execution time.<br>
</td>
</tr>
<tr nosave="" valign="top">
<td> <span style="font-style: italic;">PHG_EDGE_SIZE_THRESHOLD</span><br>
</td>
<td nosave="">Low-level parameter: Value 0.0 through 1.0, if number of vertices in
hyperedge divided by total vertices in hypergraph exceeds this
fraction, the hyperedge will be omitted.<br>
</td>
</tr>
<tr nosave="" valign="top">
<td> <span style="font-style: italic;">PHG_PROCESSOR_REDUCTION_LIMIT</span><br>
</td>
<td nosave="">Low-level parameter: In V-cycle, redistribute coarsened hypergraph to
this
fraction of processors when number of pins in coarsened hypergraph is
less than
this fraction of original number of pins. Original number of pins is
redefined
after each processor redistribution.<br>
</td>
</tr>
<tr>
</tr>
<tr>
<td valign="top"><b>Default values:</b></td>
<td><br>
</td>
</tr>
<tr>
<td><br>
</td>
<td><i>LB_APPROACH = REPARTITION<br>
</i></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_REPART_MULTIPLIER=100</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_MULTILEVEL=1 if LB_APPROACH = partition or repartition; 0 otherwise.</span></td>
</tr>
<tr>
<td><br>
</td>
<td><span style="font-style: italic;">PHG_EDGE_WEIGHT_OPERATION=max</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">ADD_OBJ_WEIGHT=none</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_CUT_OBJECTIVE=connectivity</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">CHECK_HYPERGRAPH=0</span><br>
</td>
</tr>
<tr>
<td><br>
</td>
<td><span style="font-style: italic;">PHG_OUTPUT_LEVEL=0</span></td>
</tr>
<tr>
<td><br>
</td>
<td><i>PHG_COARSENING_METHOD=agg</i></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><i>PHG_COARSEPARTITION_METHOD=auto</i></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_REFINEMENT_METHOD=fm</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><i>PHG_REFINEMENT_QUALITY=1</i></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_RANDOMIZE_INPUT=0</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_EDGE_SIZE_THRESHOLD=0.25</span></td>
</tr>
<tr>
<td style="vertical-align: top;"><br>
</td>
<td style="vertical-align: top;"><span style="font-style: italic;">PHG_PROCESSOR_REDUCTION_LIMIT=0.5</span></td>
</tr>
<tr>
<td valign="top"><b>Required Query Functions for <i>LB_METHOD = HYPERGRAPH</i>:</b></td>
<td><br>
</td>
</tr>
<tr>
<td><br>
</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 nosave="" valign="top">
<td><br>
</td>
<td nosave=""> <b><a href="ug_query_lb.html#ZOLTAN_HG_SIZE_CS_FN">ZOLTAN_HG_SIZE_CS_FN</a></b>
<br>
<b><a href="ug_query_lb.html#ZOLTAN_HG_CS_FN">ZOLTAN_HG_CS_FN</a></b>
</td>
</tr>
<tr>
<td valign="top"><b>Optional Query Functions for <i>LB_METHOD = HYPERGRAPH</i>:</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>LB_APPROACH</i>=<i>Repartition</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 <i>LB_APPROACH</i>=<i>Repartition</i> and for <a href="ug_alg.html#REMAP"><i>REMAP</i></a>=1.
</td>
</tr>
<tr>
<td><br>
</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_HG_SIZE_EDGE_WTS_FN">ZOLTAN_HG_SIZE_EDGE_WTS_FN</a></b></td>
</tr>
<tr>
<td><br>
</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_HG_EDGE_WTS_FN">ZOLTAN_HG_EDGE_WTS_FN</a></b></td>
</tr>
<tr>
<td><br>
</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_NUM_FIXED_OBJ_FN">ZOLTAN_NUM_FIXED_OBJ_FN</a></b></td>
</tr>
<tr>
<td><br>
</td>
<td><b><a href="ug_query_lb.html#ZOLTAN_FIXED_OBJ_LIST_FN">ZOLTAN_FIXED_OBJ_LIST_FN</a></b></td>
</tr>
<tr>
<td valign=top><b>Note for<br><i>LB_METHOD = HYPERGRAPH:</i></b></td>
<td><br>
</td>
</tr>
<tr>
<td><br>
</td>
<td>
It is possible to provide the graph query functions instead of the
hypergraph queries, though this is not recommended. If only graph query
functions are registered, Zoltan will automatically create a hypergraph
from the graph, but this is not equivalent to graph partitioning.
In particular, the edge weights will not be accurate.
</td>
</tr>
<tr>
<td valign="top"><b>Required Query Functions for <i>LB_METHOD = GRAPH</i>:</b></td>
<td><br>
</td>
</tr>
<tr>
<td><br>
</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 nosave="" valign="top">
<td><br>
</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 for <i>LB_METHOD = GRAPH</i>:</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>LB_APPROACH</i>=<i>Repartition</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 <i>LB_APPROACH</i>=<i>Repartition</i> and for <a href="ug_alg.html#REMAP"><i>REMAP</i></a>=1.
</td>
</tr>
</tbody>
</table>
<p>
</p>
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