A Local Graph Partitioning Heuristic Meeting Bisection Bounds

The problem of graph partitioning is of major importance for a broad range of applications. VLSI-Layout and parallel programming are only two examples where large graphs have to be cut into pieces. The partitioning of a graph into several clusters is often done by recursive bisection. Bisection heuristics are usually divided into global and local methods. Popular global methods are inertial or spectral partitioning. For a long time, the Kernighan-Lin algorithm (KL) was the only eecient local heuristic and is still widely used in several applications. Based on the idea of so called Helpful Sets, we recently proposed a new local graph bisection heuristic 3]. Helpful Sets can be used to prove upper bounds on the bisection width of regular graphs. Thus, we are able to give upper bounds on the quality of the bisections found by HS. In this paper, we will present the HS-idea, the bisection heuristic, ideas of the proofs of upper bounds, and, nally, discuss the performance of the method compared to other heuristics.