Multi-level spectral hypergraph partitioning with arbitrary vertex sizes

Authors:
Jason Y. Zien;Martine D. F. Schlag;Pak K. Chan
Affiliations:
Computer Engineering, University of California at Santa Cruz, Santa Cruz, CA;Computer Engineering, University of California at Santa Cruz, Santa Cruz, CA;Computer Engineering, University of California at Santa Cruz, Santa Cruz, CA
Venue:
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Year:
1997

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MULTI-LEVEL SPECTRAL HYPERGRAPH PARTITIONING WITH ARBITRARY VERTEX SIZES

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Abstract

This paper presents a new spectral partitioning formulation which directly incorporates vertex size information. The new formulation results in a generalized eigenvalue problem, and this problem is reduced to the standard eigenvalue problem. Experimental results show that incorporating vertex sizes into the eigenvalue calculation produces results that are 50% better than the standard formulation in terms of scaled ratio-cut cost, even when a Kernighan-Lin style iterative improvement algorithm taking into account vertex sizes is applied as a post-processing step. To evaluate the new method for use in multi-level partitioning, we combine the partitioner with a multi-level bottom-up clustering algorithm and an iterative improvement algorithm for partition refinement. Experimental results show that our new spectral algorithm is more effective than the standard spectral formulation and other partitioners in the multi-level partitioning of hypergraphs.