n-Level Hypergraph Partitioning

Abstract

We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time and thus allows very high quality. This includes a rating function that avoids nonuniform vertex weights, an efficient "semi-dynamic" hypergraph data structure, a very fast coarsening algorithm, and two new local search algorithms. One is a k-way hypergraph adaptation of Fiduccia-Mattheyses local search and gives high quality at reasonable cost. The other is an adaptation of sizeconstrained label propagation to hypergraphs. Comparisons with hMetis and PaToH indicate that the new algorithm yields better quality over several benchmark sets and has a running time that is comparable to hMetis. Using label propagation local search is several times faster than hMetis and gives better quality than PaToH for a VLSI benchmark set.

k-way Hypergraph Partitioning via n-Level Recursive Bisection

“…However, that system was very slow so that we decided to start from scratch. Our second attempt was a direct k-way n-level partitioner [33]. Despite several interesting ideas and best quality in the majority of experiments, the k-way algorithm has not been able to improve on the state of the art consistently in terms of the time-quality trade-off.…”

“…With respect to quality we could introduce V-cycles [14,30,54] and an evolutionary algorithm along the lines of KaHIP [55]. Generalizing the gain cache to direct k-way partitioning as in [33] might give good quality for large k without incurring excessive performance penalties. Having shown that our algorithm computes high quality partitions when optimizing the total cut size, future work could also look at different partitioning objectives that rely on a global view of the problem, like the (λ − 1) or sum-of-externaldegrees metric [19].…”