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Implicit Computation of Maximum Bipartite Matchings by Sublinear Functional Operations

  • Beate Bollig
  • Marc Gillé
  • Tobias Pröger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7287)

Abstract

The maximum bipartite matching problem, an important problem in combinatorial optimization, has been studied for a long time. In order to solve problems for very large structured graphs in reasonable time and space, implicit algorithms have been investigated. Any object to be manipulated is binary encoded and problems have to be solved mainly by functional operations on the corresponding Boolean functions. OBDDs are a popular data structure for Boolean functions, therefore, OBDD-based algorithms have been used as an heuristic approach to handle large input graphs. Here, two OBDD-based maximum bipartite matching algorithms are presented, which are the first ones using only a sublinear number of operations (with respect to the number of vertices of the input graph) for a problem unknown to be in NC, the complexity class that contains all problems computable in deterministic polylogarithmic time with polynomially many processors. Furthermore, the algorithms are experimentally evaluated.

Keywords

Bipartite Graph Boolean Function Input Graph Grid Graph Bipartite Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Beate Bollig
    • 1
  • Marc Gillé
    • 1
  • Tobias Pröger
    • 2
  1. 1.LS2 InformatikTU DortmundGermany
  2. 2.Institut für Theoretische InformatikETH ZürichSwitzerland

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