**METIS** is a software package for graph partitioning that implements various multilevel algorithms.^{[1]}^{[2]} METIS' multilevel approach has three phases and comes with several algorithms for each phase:

- Coarsen the graph by generating a sequence of graphs G
_{0}, G_{1}, ..., G_{N}, where G_{0}is the original graph and for each 0 ≤ i ≤ j ≤ N, the number of vertices in G_{i}is greater than the number of vertices in G_{j}. - Compute a partition of G
_{N} - Project the partition back through the sequence in the order of G
_{N}, ..., G_{0}, refining it with respect to each graph.

The final partition computed during the third phase (the refined partition projected onto G_{0}) is a partition of the original graph.

References

George Karypis & Vipin Kumar (1995). METIS - Unstructured Graph Partitioning and Sparse Matrix Ordering System, Version 2.0 (Technical report).[permanent dead link]

Karypis, G. & Kumar, V. (1999). "A fast and high quality multilevel scheme for partitioning irregular graphs". SIAM Journal on Scientific Computing. 20 (1): 359. CiteSeerX 10.1.1.39.3415. doi:10.1137/S1064827595287997.

External links

METIS website

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

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