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METIS

METIS. Three Phases Coarsening Partitioning Uncoarsening. G. Karypis , V. Kumar , “A fast and high quality multilevel scheme for partitioning irregular graphs , ” International Conference on Parallel Processing, 1995. METIS - Coarsening. Maximal Matching

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METIS

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  1. METIS • Three Phases • Coarsening • Partitioning • Uncoarsening G. Karypis, V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” International Conference on Parallel Processing, 1995.

  2. METIS - Coarsening • Maximal Matching • A set of edges without common vertices • An NP-Complete problem

  3. METIS - Partitioning • Two Steps • Randomly Choose a root • BFS to include the vertex leading less edge-cuts Root

  4. METIS - Uncoarsening • Key Idea • Each super-node comprises a set of nodes • Decrease the edge-cuts by moving a vertex to one partition to another

  5. Parallel METIS • Five Phases • Initial Partition • Coloring • Coarsening • Partitioning • Uncoarsening Each processor keeps two pieces of Information: 1. Sub-graph 2. Adjacency List G. Karypis, V. Kumar, “Parallel Multilevel k-way Partitioning Scheme for Irregular Graphs,” IEEE/ACM Conference on Supercomputing, 1996.

  6. Parallel METIS • Coloring • Adjacent vertices have different colors [Luby’s Algorithm] • The number of distinct colors used is to be minimized

  7. Parallel METIS • Coarsening Phase • Unilateral Matching • Matching Conflicts? • Why do we need coloring? Node.Match Remote Edge

  8. Parallel METIS • Partitioning Phase • Since the coarsened graph has been relatively small, partition can be done • Further parallelization is also possible G. Karypis, V. Kumar, “Parallel Multilevel k-way Partitioning Scheme for Irregular Graphs,” IEEE/ACM Conference on Supercomputing, 1996.

  9. Parallel METIS • Uncoarsening Phase • This phase is broken up into c sub-phases, where cis the number of colors • During the cthphase, all the vertices of color c are considered for movement G. Karypis, V. Kumar, “Parallel Multilevel k-way Partitioning Scheme for Irregular Graphs,” IEEE/ACM Conference on Supercomputing, 1996.

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