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

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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.

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Jian-Xin Wang, Xiao-Shuang Xu & Jian-Er Chen

  2. Department of Computer Science, Texas A&M University, College Station, TX, 77843, U.S.A.

    Jian-Er Chen

Authors
  1. Jian-Xin Wang
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  2. Xiao-Shuang Xu
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  3. Jian-Er Chen
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Corresponding author

Correspondence to Jian-Xin Wang.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant Nos. 60433020 and 60773111, the National Basic Research 973 Program of China under Grant No. 2008CB317107, the Provincial Natural Science Foundation of Hunan under Grant No. 06JJ10009, the Program for New Century Excellent Talents in University under Grant No. NCET-05-0683 and the Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0661.

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Wang, JX., Xu, XS. & Chen, JE. Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartite Graphs. J. Comput. Sci. Technol. 23, 763–768 (2008). https://doi.org/10.1007/s11390-008-9180-5

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  • DOI: https://doi.org/10.1007/s11390-008-9180-5

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