Abstract
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.
Highlights
The matching problems arise in many practical application settings where we often wish to find the proper way to pair objects or people together to achieve some desired goal
We present novel symbolic Ordered binary decision diagram (OBDD) formulation and algorithm for the optimal semimatching problem in bipartite graphs
Problem 1 (Maximum Cardinality Matching in Bipartite Graphs): The nodes are partitioned into boys and girls, and an edge can only join a boy and a girl
Summary
The matching problems arise in many practical application settings where we often wish to find the proper way to pair objects or people together to achieve some desired goal. Finding optimal semi-matching in bipartite graphs is one of typical combinatorial optimization problems, where the size of graphs is a significant and often prohibitive difficulty. This phenomenon is known as combinatorial state explosion, resulting in that large graphs cannot be stored and operated on even the largest contemporary computers. Symbolic algorithms appear to be a promising way to improve the computation of large-scale combinatorial optimization problems through encoding and searching nodes and edges implicitly. Our contribution is to present the symbolic algorithm for optimal semi-matching in bipartite graphs. The symbolic formulations for bipartite graphs and optimal semi-matching are described in Section 3; Section 4 presents the symbolic OBDD algorithm; The last Section gives experimental results and analysis
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
