Implicit Computation of Maximum Bipartite Matchings by Sublinear Functional Operations
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.
KeywordsBipartite Graph Boolean Function Input Graph Grid Graph Bipartite Match
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- 11.Charles, D.X., Chickering, M., Devanur, N.R., Jain, K., Sanghi, M.: Fast algorithms for finding matchings in lopsided bipartite graphs with applications to display ads. In: Proc. of ACM Conference on Electronic Commerce 2010, pp. 121–128 (2010)Google Scholar
- 14.Gentilini, R., Piazza, C., Policriti, A.: Computing strongly connected components in a linear number of symbolic steps. In: Proc. of SODA, pp. 573–582. ACM Press (2003)Google Scholar
- 23.Negruseri, C.S., Pasoi, M.B., Stanley, B., Stein, C., Strat, C.G.: Solving maximum flow problems on real world bipartite graphs. In: Proc. of ALENEX, pp. 14–28. SIAM (2009)Google Scholar
- 27.Sawitzki, D.: Implicit simulation of FNC algorithms. ECCC Report TR07-028 (2007)Google Scholar
- 29.Wegener, I.: Branching Programs and Binary Decision Diagrams - Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications (2000)Google Scholar