METIS Three Phases Coarsening Partitioning Uncoarsening

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Presentation transcript:

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 A set of edges without common vertices An NP-Complete problem

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

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

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.

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

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

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

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