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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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Presentation Transcript
slide1

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.

slide2

METIS - Coarsening

  • Maximal Matching
    • A set of edges without common vertices
    • An NP-Complete problem
slide3

METIS - Partitioning

  • Two Steps
    • Randomly Choose a root
    • BFS to include the vertex leading less edge-cuts

Root

slide4

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
slide5

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.

slide6

Parallel METIS

  • Coloring
    • Adjacent vertices have different colors [Luby’s Algorithm]
    • The number of distinct colors used is to be minimized
slide7

Parallel METIS

  • Coarsening Phase
    • Unilateral Matching
      • Matching Conflicts?
      • Why do we need coloring?

Node.Match

Remote Edge

slide8

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.

slide9

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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