Efficient Matching for Column Intersection Graphs

Abstract

To improve the quality and efficiency of hypergraph-based matrix partitioners, we investigate high-quality matchings in column intersection graphs of large sparse binary matrices. We show that such algorithms have a natural decomposition in an integer-weighted graph-matching function and a neighbor-finding function and study the performance of 16 combinations of these functions. We improve upon the original matching algorithm of the Mondriaan matrix partitioner: by using PGA’, we improve the average matching quality from 95.3% to 97.4% of the optimum value; by using our new neighbor-finding heuristic, we obtain comparable quality and speedups of up to a factor of 19.6.