METIS

METIS is a software package for graph partitioning that implements various multilevel algorithms.

METIS' multilevel approach has three phases and comes with several algorithms for each phase:

1. Coarsen the graph by generating a sequence of graphs G₀, G₁, ..., G_N, where G₀ 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.
2. Compute a partition of G_N
3. Project the partition back through the sequence in the order of G_N, ..., G₀, refining it with respect to each graph.

The final partition computed during the third phase (the refined partition projected onto G₀) is a partition of the original graph.