Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartit

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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 ∈ > 0, if an instance of the Min-CVCB problem has a minimum vertex cover of size (ku, kl), our algorithm constructs a vertex cover of size (ku*, kl*), satisfying max{ku*/ku, kl*/kl} ≤ 1 + ∈.
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