Download PDF - An approximation algorithm for the total covering problemAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

An approximation algorithm for the total covering problem

Authors 1

Affiliations

  1. Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

Abstract

We introduce a 2-factor approximation algorithm for the minimum total covering number problem.

Keywords

ENG
covering, total covering, approximation algorithm

Bibliography

  1. Y. Alavi, M. Behzad, L.M. Leśniak-Foster and E.A. Nordhaus, Total matchings and total coverings of graphs, J. Graph Theory 1 (1977) 135-140, doi: 10.1002/jgt.3190010209.
  2. Y. Alavi, J. Liu, F.J. Wang and F.Z. Zhang, On total covers of graphs, Discrete Math. 100 (1992) 229-233. Special volume to mark the centennial of Julius Petersen's ``Die Theorie der regulären Graphs'', Part I, doi: 10.1016/0012-365X(92)90643-T.
  3. I. Dinur and S. Safra, On the hardness of approximating minimum vertex cover, Annals of Mathematics 162 (2005) 439-485, doi: 10.4007/annals.2005.162.439.
  4. R. Duh and M. Fürer, Approximation of k-set cover by semi-local optimization, Proceedings of STOC '97: the 29th Annual ACM Symposium on Theory of Computing, (1997) 256-264.
  5. P. Erdös and A. Meir, On total matching numbers and total covering numbers of complementary graphs, Discrete Math. 19 (1977) 229-233, doi: 10.1016/0012-365X(77)90102-9.
  6. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs, vol. 208 of Monographs and Textbooks in Pure and Applied Mathematics (Marcel Dekker Inc., New York, 1998).
  7. S.M. Hedetniemi, S.T. Hedetniemi, R. Laskar, A. McRae and A. Majumdar, Domination, independence and irredundance in total graphs: a brief survey, in: Y. Alavi and A. Schwenk, eds, Graph Theory, Combinatorics and Applications: Proceedings of the 7th Quadrennial International Conference on the Theory and Applications of Graphs 2 (1995) 671-683. John Wiley and Sons, Inc.
  8. D.S. Johnson, Approximation algorithms for combinatorial problems, Journal of Computer and System Sciences (1974) 256-278, doi: 10.1016/S0022-0000(74)80044-9.
  9. S. Khot and O. Regev, Vertex cover might be hard to approximate within 2-ε, in: Proceedings of the 17th IEEE Conference on Computational Complexity (2002) 379-386.
  10. A. Majumdar, Neighborhood hypergraphs, PhD thesis, Clemson University, Department of Mathematical Sciences, 1992.
  11. D.F. Manlove, On the algorithmic complexity of twelve covering and independence parameters of graphs, Discrete Appl. Math. 91 (1999) 155-177, doi: 10.1016/S0166-218X(98)00147-4.
  12. A. Meir, On total covering and matching of graphs, J. Combin. Theory (B) 24 (1978) 164-168, doi: 10.1016/0095-8956(78)90017-5.
  13. U. Peled and F. Sun, Total matchings and total coverings of threshold graphs, Discrete Appl. Math. 49 (1994) 325-330. Viewpoints on optimization (Grimentz, 1990; Boston, MA, 1991).
Discussiones Mathematicae Graph Theory
2007/27/3
Export to PBN, Opens in new tab
Pages:
553-558
Main language of publication
English
Received
2006-09-20
Accepted
2006-12-30
Published
2007

DOI: 10.7151/dmgt.1380

Exact and natural sciences