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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Chen J, Kanj I A. Constrained minimum vertex cover in bipartite graphs: Complexity and parameterized algorithms. Journal of Computer and System Science, 2003, 67(4): 833–847.
Hasan N, Liu C L. Minimum fault coverage in reconfigurable arrays. In Proc. 18th Int. Symp. Fault-Tolerant Computing (FTCS’88), Los Alamitos, CA, 1988, pp.348–353.
Nilsson N J. Principles of Artificial Intelligence. Palo Alto: Tioga Publishing Co., CA, 1980.
Blough D M. On the reconfigurable of memory arrays containing clustered faults. In Proc. 21st Int. Symp. Fault-Tolerant Computing (FTCS’91), Montreal, Canada, 1991, pp.444–451.
Blough D M, Pelc A. Complexity of fault diagnosis in comparison models. IEEE Trans. Comput., 1992, 41(3): 318–323.
Hasan N, Liu C L. Fault covers in reconfigurable PLAs. In Proc. 20th Int. Symp. Fault-Tolerant Computing (FTCS’90), Newcastle upon Tyne, 1990, pp.166–173.
Kuo S Y, Fuchs W K. Efficient spare allocation for reconfigurable arrays. IEEE Des. Test, 1987, 4(1): 24–31.
Low C P, Leong H W. A new class of efficient algorithms for reconfiguration of memory arrays. IEEE Trans. Comput., 1996, 45(1): 614–618.
Smith M D, Mazumder P. Generation of minimal vertex cover for row/column allocation in self-repairable arrays. IEEE Trans. Comput., 1996, 45(1): 109–115.
Fernau H, Niedermeier R. An efficient exact algorithm for constraint bipartite vertex cover. J. Algorithms, 2001, 38(2): 374–410.
Downey R, Fellows M. Parameterized Complexity. Berlin: Springer, 1999.
Cormen T H, Leiserson C E, Rovest R L. Introduction to Algorithms. New York: McGraw-Hill Book Company, 1992.
Lovasz L, Plummer M D. Matching Theory. Amsterdam: North-Holland, 1986.
Author information
Authors and Affiliations
Corresponding author
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.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
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
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11390-008-9180-5