METIS
Graph Partioning, Mesh Partitioning, Matrix Reordering


METIS is a C program which can partition a graph, partition a finite element mesh, or reorder a sparse matrix.

Typically, the graph or mesh is being partitioned so that a computational task can be correspondingly divided up among a number of processors for parallel computing. Thus, it is important that each part of the partition have roughly the same number of elements, and that "connections" between distinct partitions be limited, as much as possible, to reduce the amount of interprocess communication necessary.

The reordering of a sparse matrix is done in order to control the size of the active front, and to reduce the number of fill-in entries created during elimination. In this case, the reordering is very useful even when the computation is to be done on a single processor.

METIS consists of a fundamental library, and a number of executable programs (which call appropriate routines from the library), to handle the graph partitioning, mesh partitioning, and matrix reordering tasks. A number of other utilities are also included.

METIS uses particular formats for storing the graph, mesh or matrix data. The formats have extended to include the ability to weight certain items.

METIS can be executed on a single processor. However, METIS includes an MPI interface which allows it to be run in parallel as well.

Most users will be interested in running one of the executable programs associated with the METIS library, rather than using the library directly. For this purpose, you should go to the web pages listed below, which are associated directly with

Licensing:

METIS is part of the METIS family of Multilevel Partitioning Algorithms. It was produced by the lab of George Karypis, who states

"It is our general policy to make these tools available to the research community for use in their own research and/or non-commercial applications."

For further information on licensing and permissions, refer to http://www.cs.umn.edu/~metis, the METIS home page.

Languages:

METIS is available in a C version.

Related Programs:

GRAPHCHK, a C program which can read a METIS GRAPH file and verify that it has the proper format.

KMETIS, a C program which can partition the nodes of a graph.

MESH2DUAL, a C program which converts a finite element mesh to a graph, for further processing by KMETIS or PMETIS.

MESH2NODAL, a C program which converts a finite element mesh to a graph, for further processing by KMETIS or PMETIS.

METIS_GRAPH, a data directory which contains examples of the graph files used to describe a graph to the METIS family of programs.

METIS_MESH, a data directory which contains examples of the mesh files used to describe a finite element mesh to the METIS family of programs.

MPI, a message passing interface that allows programs to be written for execution on parallel computers.

NEIGHBORS_TO_METIS_GRAPH, a FORTRAN90 program which reads information describing the adjacency relations in a tet mesh, and writes out essentially the same information, but in a format that METIS will accept.

OEMETIS, a C program which reads the adjacency graph of a sparse matrix, stored in METIS GRAPH format, and produces a reordering of the nodes to minimize fill.

ONMETIS, a C program which reads the adjacency graph of a sparse matrix, stored in METIS GRAPH format, and produces a reordering of the nodes to minimize fill.

PARTDMESH, a C program which can partition the elements of a finite element mesh, by working with the dual graph of the mesh.

PARTNMESH, a C program which can partition the elements of a finite element mesh, by working with the nodal graph of the mesh.

Reference:

  1. George Karypis, Vipin Kumar,
    METIS, a Software Package for Partitioning Unstructured Graphs and Computing Fill-Reduced Orderings of Sparse Matrices;
  2. George Karypis, Vipin Kumar,
    A fast and high quality multilevel scheme for partitioning irregular graphs,
    SIAM Journal on Scientific Computing,
    Volume 20, Number 1, 1998, pages 359-392;

Source Code:

Examples and Tests:

You can go up one level to the C source codes.


Last revised on 27 April 2006.