The Symbolic OBDD Algorithm for Finding Optimal Semi-matching in Bipartite Graphs
Tianlong Gu, Liang Chang, Zhoubo Xu
DOI: 10.4236/cn.2011.32009   PDF   HTML     4,645 Downloads   8,485 Views   Citations


The optimal semi-matching problem is one relaxing form of the maximum cardinality matching problems in bipartite graphs, and finds its applications in load balancing. Ordered binary decision diagram (OBDD) is a canonical form to represent and manipulate Boolean functions efficiently. OBDD-based symbolic algorithms appear to give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic OBDD formulation and algorithm for the optimal semi-matching problem in bipartite graphs. The symbolic algorithm is initialized by heuristic searching initial matching and then iterates through generating residual network, building layered network, backward traversing node-disjoint augmenting paths, and updating semi-matching. It does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Our simulations show that symbolic algorithm has better performance, especially on dense and large graphs.

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T. Gu, L. Chang and Z. Xu, "The Symbolic OBDD Algorithm for Finding Optimal Semi-matching in Bipartite Graphs," Communications and Network, Vol. 3 No. 2, 2011, pp. 65-72. doi: 10.4236/cn.2011.32009.

Conflicts of Interest

The authors declare no conflicts of interest.


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