1. Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartite Graphs
- Author
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Jianxin Wang, Jianer Chen, and Xiao-Shuang Xu
- Subjects
Vertex (graph theory) ,Mathematical optimization ,Matching (graph theory) ,Computer science ,Vertex cover ,Implication graph ,Approximation algorithm ,Complete bipartite graph ,Edge cover ,Computer Science Applications ,Theoretical Computer Science ,Vertex (geometry) ,Combinatorics ,Computational Theory and Mathematics ,Hardware and Architecture ,Bipartite graph ,Feedback vertex set ,Software ,Blossom algorithm - Abstract
The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the technique of chain implication. For any given constant ɛ > 0, if an instance of the Min-CVCB problem has a minimum vertex cover of size (k u , k l ), our algorithm constructs a vertex cover of size (k * u , k * l ), satisfying max {k * u /k u , k * l /k l } ≤ 1 + ɛ.
- Published
- 2008
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