`ISRN Discrete MathematicsVolume 2011 (2011), Article ID 213084, 10 pageshttp://dx.doi.org/10.5402/2011/213084`
Research Article

## An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs

1Department of Mathematics, Narajole Raj College, Paschim Medinipur Narajole 721 211, India
2Department of Mathematics, National Institute of Technology, Durgapur 713209, India
3Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721 102, India

Received 16 July 2011; Accepted 29 August 2011

Academic Editors: Q. Gu, U. A. Rozikov, and R. Yeh

Copyright © 2011 Akul Rana et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. J. A. Horne and J. C. Smith, “Dynamic programming algorithms for the conditional covering problem on path and extended star graphs,” Networks, vol. 46, no. 4, pp. 177–185, 2005.
2. D. G. Corneil and P. A. Kamula, “Extensions of permutation and interval graphs,” in Proceedings of the 18th Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, Fla., 1987), Congr. Numer. 58, pp. 267–275, 1987.
3. I. Dagan, M. C. Golumbic, and R. Y. Pinter, “Trapezoid graphs and their coloring,” Discrete Applied Mathematics, vol. 21, no. 1, pp. 35–46, 1988.
4. F. Cheah and D. G. Corneil, “On the structure of trapezoid graphs,” Discrete Applied Mathematics, vol. 66, no. 2, pp. 109–133, 1996.
5. T. H. Ma and J. P. Spinrad, “On the $2$-chain subgraph cover and related problems,” Journal of Algorithms, vol. 17, no. 2, pp. 251–268, 1994.
6. I. D. Moon and S. S. Chaudhry, “An analysis of network location problems with distance constraints,” Management Science, vol. 30, no. 3, pp. 290–307, 1984.
7. S. S. Chaudhry, “New heuristics for the conditional covering problem,” Opsearch, vol. 30, pp. 42–47, 1993.
8. S. S. Chaudhry, I. D. Moon, and S. T. McCormick, “Conditional covering: greedy heuristics and computational results,” Computers & Operations Research, vol. 14, no. 1, pp. 11–18, 1987.
9. V. Lotfi and I. D. Moon, “Hybrid heuristics for conditional covering problems,” International Journal of Modelling and Simulation, vol. 17, no. 3, pp. 185–190, 1997.
10. I. D. Moon, “Conditional covering: worst case analysis of greedy heuristics,” Journal of the Korean Operations Research and Management Science Society, vol. 15, no. 2, pp. 97–104, 1990.
11. I. D. Moon and L. Papayanopoulos, “Facility location on a tree with maximum distance constraints,” Computers & Operations Research, vol. 22, no. 9, pp. 905–914, 1995.
12. J. A. Horne and J. C. Smith, “A dynamic programming algorithm for the conditional covering problem on tree graphs,” Networks, vol. 46, no. 4, pp. 186–197, 2005.
13. B. J. Lunday, J. C. Smith, and J. B. Goldberg, “Algorithms for solving the conditional covering problem on paths,” Naval Research Logistics, vol. 52, no. 4, pp. 293–301, 2005.
14. B. Sivan, S. Harini, and C. Pandu Rangan, “On conditional covering problem,” Mathematics in Computer Science, vol. 3, no. 1, pp. 97–107, 2010.
15. A. Rana, A. Pal, and M. Pal, “The conditional covering problem on unweighted interval graphs,” Journal of Applied Mathematics and Informatics, vol. 28, pp. 1–11, 2010.
16. M. I. Abouelhoda and E. Ohlebusch, “Chaining algorithms for multiple genome comparison,” Journal of Discrete Algorithms, vol. 3, no. 2–4, pp. 321–341, 2005.
17. M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, NY, USA, 1980.