## Quality Matching and Local Improvement for Multilevel Graph-Partitioning (1999)

Citations: | 28 - 8 self |

### BibTeX

@MISC{Monien99qualitymatching,

author = {Burkhard Monien and Robert Preis and Ralf Diekmann},

title = {Quality Matching and Local Improvement for Multilevel Graph-Partitioning},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

Multilevel strategies have proven to be very powerful approaches in order to partition graphs efficiently. Their efficiency is dominated by two parts; the coarsening and the local improvement strategies. Several methods have been developed to solve these problems, but their efficiency has only been proven on an experimental basis. In this paper we present new and efficient methods for both problems, while satisfying certain quality measurements. For the coarsening part we develop a new approximation algorithm for maximum weighted matching in general edge-weighted graphs. It calculates a matching with an edge weight of at least 1 2 of the edge weight of a maximum weighted matching. Its time complexity is O(jEj), with jEj being the number of edges in the graph. Furthermore, we use the Helpful-Set strategy for the local improvement of partitions. For partitioning graphs with a regular degree of 2k into 2 parts, it guarantees an upper bound of k\Gamma1 2 jV j + 1 on the cut size of th...