A tight analysis of the maximal matching heuristic

Lecture Notes in Computer Science

Volumn 3595, Issue , 2005, Pages 701-709

  Cardinal, Jean ^a   Labbé, Martine ^a   Langerman, Stefan ^a   Levy, Eythan ^a   Mélot, Hadrien ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF MONS   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; GRAPH THEORY; PROBLEM SOLVING; ARTIFICIAL INTELLIGENCE; COMPUTERS;

MAXIMAL MATCHING HEURISTIC; WORST-CASE PERFORMANCE; APPROXIMATION RATIOS; AVERAGE DEGREE; MINIMUM DEGREE; MINIMUM MAXIMAL MATCHING; MINIMUM VERTEX COVER;

HEURISTIC METHODS; COMBINATORIAL MATHEMATICS;

EID: 26844431961     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11533719_71     Document Type: Conference Paper

References (19)

1. R. Bar-Yehuda and S.Even. A local-ratio theorem for approximating the weighted vertex cover problem. Ann. Discrete Math., 25:27-45, 1985.
2. J. Cardinal, M. Labbé, S. Langerman, E. Levy, and H. Mélot. A tight analysis of the maximal matching heuristic. Technical Report 545, Université Libre de Bruxelles, 2005. Available at http://www.ulb.ac.be/ di/publications.
3. M. Chlebìk and J. Chlebìková. Approximation hardness of minimum edge dominating set and minimum maximal matching. In Proceedings of 14th International Symposium on Algorithms and Computation (ISAAC), Lecture Notes in Computer Science. Springer-Verlag, 2003.
4. J. Christophe, S. Dewez, J. Doignon, S. Elloumi, G. Fasbender, P. Grégoire, D. Huygens, M. Labbé, H. Mélot, and H. Yaman. Linear inequalities among graph invariants: using GraPHedron to uncover optimal relationships. Submitted. Available at http://www.optimization-online.org/ DB_HTML/2004/09/964.html, 2004.
5. A. Clementi and L. Trevisan. Improved non-approximability results for vertex cover problems with density constraints. Theoretical Computer Science, 225(1-2):113-128, 1999.
6. R. Diestel. Graph Theory, Second Edition. Springer-Verlag, 2000.
7. A.V. Eremeev. On some approximation algorithms for dense vertex cover problem. In Proceedings of SOR. Springer-Verlag, 1999.
8. M. R. Garey and D. S. Johnson. Computers and intractability. A guide to the theory of NP-completeness. Freeman and Company, 1979.
9. E. Halperin. Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs. Siam Journal on Computing, 31:1608-1623, 2002.
10. P. Hansen and H. Mélot. Variable neighborhood search for extremal graphs 9. Bounding the irregularity of a graph. To appear in S. Fajtlowicz et al. (Eds.), Graphs and Discovery, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, (forthcoming), Providence, American Mathematical Society.
11. J. Hastad. Some optimal inapproximability results. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 1-10, 1997.
12. T. Ibaraki and H. Nagamochi. An approximation of the minimum vertex cover in a graph. Japan J. Indust. Appl. Math., 16:369-375, 1999.
13. T. Imamura and K. Iwama. Approximating vertex cover on dense graphs. In Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2005.
14. G. Karakostas. A better approximation ratio for the vertex cover problem. ECCC Report TR04-084, 2004.
15. M. Karpinski and A. Zelikovsky. Approximating dense cases of covering problems. In P. Pardalos and D. Du, editors, Proceedings of the DIMACS Workshop on Network Design: Connectivity and Facilites Location, volume 40 of DIMACS series in Disc. Math. and Theor. Comp. Sci., pages 169-178, 1997.
16. H. Mélot. Facets defining inequalities among graph invariants: the system GraPHedron. In preparation.
17. B. Monien and E. Speckenmeyer. Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Inf., 22:115-123, 1985.
18. C. H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. J. Comput. System. Sci., 43(3):425-440, 1991.
19. M. Yannakakis and F. Gavril. Edge dominating sets in graphs. SIAM J. Appl. Math., 38(3):364-372, 1980.