On coloring unit disk graphs

Algorithmica (New York)

Volumn 20, Issue 3, 1998, Pages 277-293

  Graf A ^a   Stumpf, M ^a   Weissenfels G ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Approximation algorithm; Channel assignment problem; Graph coloring; Unit disk graphs

Indexed keywords

EID: 0001388944     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009196     Document Type: Article

References (20)

1. H. Breu and D. G. Kirkpatrick. Unit disk graph recognition is NP-hard. Technical Report 93-27, Department of Computer Science, University of British Columbia, 1993.
2. B. N. Clark, C. J. Colbourn, and D. S. Johnson. Unit disk graphs. Discrete Mathematics, 86:165-177, 1990.
3. S. Even. Graph Algorithms. Pitman, London, 1979.
4. L. Ford and D. Fulkerson. Flows in Networks. Princeton University Press, Princeton, NJ, 1962.
5. M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoretical Computer Science, 1:237-267, 1976.
6. M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Computer Science and Applied Mathematics. Academic Press, New York, 1980.
7. A. Gräf. Permutative graph colorings. Musikinformatik und Medientechnik 5/92, Johannes Gutenberg-Universität, Musikwissenschaftliches Institut, Bereich Musikinformatik, Mainz, 1992.
8. A. Gräf. Coloring and Recognizing Special Graph Classes. Ph.D. thesis, Johannes Gutenberg-Universität, Mainz, 1995.
9. Published as Report No. 20/95 in the series Musikinformatik und Medientechnik.
10. A. Gräf, M. Stumpf, and G. Weißenfels. On coloring unit disk graphs. Musikinformatik und Medientechnik 17/94, Johannes Gutenberg-Universität, Musikwissenschaftliches Institut, Bereich Musikinformatik, Mainz, 1994.
11. W. Hale. Frequency assignment: Theory and applications. Proceedings of the IEEE, 68:1497-1514, 1980.
12. 5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 2:225-231, 1973.
13. C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. In Proc. 25th Annual ACM Symposium on the Theory of Computing, pages 286-293. ACM, New York, 1993.
14. E. Malesinska, S. Piskorz, and G. Weißenfels. On the approximability of coloring problems for disk graphs. Musikinformatik und Medientechnik 26/96, Johannes Gutenberg-Universität, Musikwissenschaftliches Institut, Bereich Musikinformatik, Mainz, 1996.
15. M. V. Marathe, H. Breu, H. B. Hunt III, S. S. Ravi, and D. J. Rosenkrantz. Simple heuristics for unit disk graphs. Unpublished manuscript (see also [15]).
16. M. V. Marathe, H. B. Hunt III, and S. S. Ravi. Geometry based approximations for intersection graphs. In Proc. Fourth Canadian Conference on Computational Geometry, pages 244-249, 1992.
17. D. W. Matula and L. L. Beck. Smallest-last ordering and clustering and graph coloring algorithms. Journal of the Association of Computing Machinery, 30(3):417-427, 1983.
18. D. W. Matula, G. Marble, and J. Isaacson. Graph coloring algorithms. In R. C. Read, editor, Graph Theory and Computing, pages 108-122. Academic Press, New York, 1972.
19. R. H. Möhring. Algorithmic aspects of comparability graphs and interval graphs. In I. Rival, editor, Graphs and Orders, pages 41-101. Reidel, Dordrecht, 1985.
20. R. Peeters. On coloring j-unit sphere graphs. FEW 512, Department of Economics, Tilburg University, 1991.