An Improved Boolean Circuit for Maximum Matching in a Convex Bipartite Graph

  • Authors:

  • Eunhui Park;Kunsoo Park

  • Affiliations:

  • Department of Computer Science, University of Maryland College Park, MD 20742, USA. E-mail: ehpark@cs.umd.edu;School of Computer Science and Engineering, Seoul National University Seoul 151-744, Korea. E-mail: kpark@theory.snu.ac.kr

  • Venue:
  • Fundamenta Informaticae - Workshop on Combinatorial Algorithms
  • Year:
  • 2008

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Abstract

The Boolean circuit is a simple and realistic model for parallel computation. Chung and Lee considered the problem of finding a maximum matching in a convex bipartite graph, which has two sets of vertices, A and B, such that for any vertex v of A, the neighbors of v in B are contiguous. They gave a Boolean circuit for the problem in O(log$^2$ n+log n· log log n· log b) depth and O(bn$^3$) size, where n is the number of vertices in set A of the convex bipartite graph and b is the number of bits representing a vertex. Using Boolean circuits of prefix computation, odd-even merge, and some other parallel techniques, we present an improved Boolean circuit for the same problem in O(log$^2$ n · (log b + log log n)) depth and O(bn$^2$ log n) size.