Approximation algorithms for finding and partitioning unit-disk graphs into co-k-plexes

Optimization Letters

Volumn 4, Issue 3, 2010, Pages 311-320

  Balasundaram, Balabhaskar ^a   Chandramouli, Shyam Sundar ^b   Trukhanov, Svyatoslav ^c  

^a Oklahoma State University   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

^c MICROSOFT   (United States)

Author keywords

Co k plex; Defective coloring; Graph coloring; Independent set; k dependent set; t improper coloring; Unit disk graph

Indexed keywords

CO-K-PLEX; DEFECTIVE COLORING; GRAPH COLORINGS; INDEPENDENT SET; K-DEPENDENT SET; T-IMPROPER COLORING; UNIT DISK GRAPHS;

DISKS (STRUCTURAL COMPONENTS); GRAPH THEORY;

APPROXIMATION ALGORITHMS;

EID: 77955848556     PISSN: 18624472     EISSN: 18624480     Source Type: Journal    
DOI: 10.1007/s11590-009-0146-5     Document Type: Article

References (28)

1. Andrews J., Jacobson M.: On a generalization of chromatic number. Congressus Numerantium 47, 33-48 (1985).
2. Balasundaram, B.: Graph theoretic generalizations of clique: optimization and extensions. Ph. D. dissertation, Texas A& M University (2007).
3. Balasundaram B., Butenko S.: Optimization problems in unit-disk graphs. In: Floudas, C. A., Pardalos, P. M. (eds) Encyclopedia of Optimization., Springer Science+Business Media, New York (2008) (to appear).
4. Balasundaram, B., Butenko, S., Hicks, I. V.: Clique relaxations in social network analysis: the maximum k-plex problem (2008). http://iem. okstate. edu/baski/files/kplex4web. pdf (submitted).
5. Breu H., Kirkpatrick D. G.: Unit disk graph recognition is NP-hard. Comput. Geom. Theory Appl. 9(1-2), 3-24 (1998).
6. Cerioli, M. R., Faria, L., Ferreira, T. O., Protti, F.: On minimum clique partition and maximum independent set on unit disk graphs and penny graphs: complexity and approximation. In: Latin-American Conference on Combinatorics, Graphs and Applications, Electronic Notes in Discrete Mathematics, vol. 18, pp. 73-79 (electronic). Elsevier, Amsterdam (2004).
7. Clark B. N., Colbourn C. J., Johnson D. S.: Unit disk graphs. Discrete Math. 86, 165-177 (1990).
8. Cook W., Cunningham W., Pulleyblank W., Schrijver A.: Combinatorial Optimization. Wiley, New York (1998).
9. Cowen L., Cowen R., Woodall D.: Defective colorings of graphs in surfaces: partitions into subgraphs of bounded valence. J. Graph Theory 10, 187-195 (1986).
10. Cowen L., Goddard W., Jesurum C. E.: Defective coloring revisited. J. Graph Theory 24(3), 205-219 (1997).
11. Dessmark, A., Jansen, K., Lingas, A.: The maximum k-dependent and f-dependent set problem. In: Ng, K. W., Raghavan, P., Balasubramanian, N. V., Chin, F. Y. L. (eds.) Proceedings of the 4th International Symposium on Algorithms and Computation: ISAAC '93. Lecture Notes in Computer Science, vol. 762, pp. 88-97. Springer, Berlin (1993).
12. Djidev, H., Garrido, O., Levcopoulos, C., Lingas, A.: On the maximum k-dependent set problem. Tech. Rep. LU-CS-TR: 92-91, Dept. of Computer Science, Lund University, Sweden (1992).
13. Erlebach T., Fiala J.: Independence and coloring problems on intersection graphs of disks. In: Bampis, E., Jansen, K., Kenyon, C. (eds) Efficient Approximation and Online Algorithms. Lecture Notes in Computer Science, vol. 3484, pp. 135-155. Springer, Heidelberg (2006).
14. Fishkin, A. V.: Disk graphs: a short survey. In: Jansen, K., Solis-Oba, R. (eds.) Approximation and Online Algorithms. Lecture Notes in Computer Science, vol. 2909, pp. 260-264. Springer, Berlin (2004).
15. Garey M. R., Johnson D. S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman and Company, New York (1979).
16. Hale W. K.: Frequency assignment: theory and applications. Proc IEEE 68(12), 1497-1514 (1980).
17. Harary F., Jones K.: Conditional colorability ii: Bipartite variations. Congressus Numerantium 50, 205-218 (1985).
18. 1-ε. Acta Math. 182, 105-142 (1999).
19. Havet F., Kang R. J., Sereni J. S.: Improper colouring of unit disk graphs. Elect. Notes Discrete Math. 22, 123-128 (2005).
20. Havet, F., Kang, R. J., Sereni, J. S.: Improper colouring of unit disk graphs. Tech. Rep. RR-6206, Institute National de Recherche en Informatique et en Automatique (INRIA), France (2007) Networks (to appear). http://hal. inria. fr/inria-00150464_v2/.
21. Hochbaum D. S.: Efficient bounds for the stable set, vertex cover and set packing problems. Discrete Appl. Math. 6(3), 243-254 (1983).
22. Hunt H. B., Marathe M. V., Radhakrishnan V., Ravi S. S., Rosenkrantz D. J., Stearns R. E.: NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs. J. Algorithms 26(2), 238-274 (1998).
23. Kang, R.: Improper coloring of graphs. Ph. D. dissertation, University of Oxford (2007).
24. Krishna P., Vaidya N. H., Chatterjee M., Pradhan D. K.: A cluster-based approach for routing in dynamic networks. ACM SIGCOMM Comp. Commun. Rev. 27(2), 49-64 (1997).
25. Marathe M. V., Breu H., Hunt H. B. III, Ravi S. S., Rosenkrantz D. J.: Simple heuristics for unit disk graphs. Networks 25, 59-68 (1995).
26. Ramaswami, R., Parhi, K. K.: Distributed scheduling of broadcasts in a radio network. In: Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM '89), vol. 2, pp. 497-504 (1989).
27. Seidman S. B., Foster B. L.: A graph theoretic generalization of the clique concept. J. Math. Sociol. 6, 139-154 (1978).
28. Szekeres G., Wilf H. S.: An inequality for the chromatic number of a graph. J. Comb. Theory 4, 1-3 (1968).