# METIS - Serial Graph Partitioning and Fill-reducing Matrix Ordering

METIS stable version: 5.1.0, 3/30/2013; MT-METIS version: 0.6.0, 10/30/2016

METIS is a set of serial programs for partitioning graphs, partitioning finite element meshes, and producing fill reducing orderings for sparse matrices. The algorithms implemented in METIS are based on the multilevel recursive-bisection, multilevel *k*-way, and multi-constraint partitioning schemes developed in our lab.

METIS's key features are the following:

Provides high quality partitions! |
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Experiments on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation show that METIS produces partitions that are consistently better than those produced by other widely used algorithms. The partitions produced by METIS are consistently 10% to 50% better than those produced by spectral partitioning algorithms. |

It is extremely fast! |

Experiments on a wide range of graphs has shown that METIS is one to two orders of magnitude faster than other widely used partitioning algorithms. Graphs with several millions of vertices can be partitioned in 256 parts in a few seconds on current generation workstations and PCs. |

Produces low fill orderings! |

The fill-reducing orderings produced by METIS are significantly better than those produced by other widely used algorithms including multiple minimum degree. For many classes of problems arising in scientific computations and linear programming, METIS is able to reduce the storage and computational requirements of sparse matrix factorization, by up to an order of magnitude. Moreover, unlike multiple minimum degree, the elimination trees produced by METIS are suitable for parallel direct factorization. Furthermore, METIS is able to compute these orderings very fast. Matrices with millions of rows can be reordered in just a few seconds on current generation workstations and PCs. |

Note that if quality is of outmost importance to your application (whereas computationally efficiency is not as critical), I suggest you use the hMETIS tool to compute the partitioning. In this case, you just need to treat your graph as a (rather simple) hypergraph.