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