Abstract
We present the first location-oblivious distributed unit disk graph coloring algorithm having a provable performance ratio of three (i.e. the number of colors used by the algorithm is at most three times the chromatic number of the graph). This is an improvement over the standard sequential coloring algorithm that has a worst case lower bound on its performance ratio of 4−3/k (for any k>2, where k is the chromatic number of the unit disk graph achieving the lower bound) (Tsai et al., in Inf. Process. Lett. 84(4):195–199, 2002). We present a slightly better worst case lower bound on the performance ratio of the sequential coloring algorithm for unit disk graphs with chromatic number 4. Using simulation, we compare our algorithm with other existing unit disk graph coloring algorithms.
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Breu, H., Kirkpatrick, D.G.: Unit disk graph recognition is np-hard. Comput. Geom. Theory Appl. 9(1–2), 3–24 (1998)
Erlebach, T., Fiala, J.: Independence and coloring problems on intersection graphs of disks. In: Approximation Algorithms in Combinatorial Optimization. Lecture Notes in Computer Science, vol. 3484, pp. 135–155. Springer, Berlin (2006)
Gräf, A., Stumpf, M., Weißenfels, G.: On coloring unit disk graphs. Algorithmica 20(3), 277–293 (1998)
Hale, W.K.: Frequency assignment: theory and applications. In: Proceedings of the IEEE, vol. 68, pp. 1497–1514 (1980)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum, New York (1972)
Marathe, M., Breu, H., Ravi, S., Rosenkrantz, D.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)
Matula, D.W., Beck, L.L.: Smallest-last ordering and clustering and graph coloring algorithms. J. ACM 30(3), 417–427 (1983)
Peeters, R.: On coloring j-unit sphere graphs. Technical Report FEW 512, Department of Economics, Tilburg University, Tilburg, The Netherlands (1991)
Raghavan, V., Spinrad, J.: Robust algorithms for restricted domains. J. Algorithms 48(1), 160–172 (2003)
Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley, New York (2006)
Tsai, Y., Lin, Y., Hsu, F.: The online first-fit algorithm for radio frequency assignment problems. Inf. Process. Lett. 84(4), 195–199 (2002)
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Barbeau, M., Bose, P., Carmi, P. et al. Location-Oblivious Distributed Unit Disk Graph Coloring. Algorithmica 60, 236–249 (2011). https://doi.org/10.1007/s00453-009-9334-z
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DOI: https://doi.org/10.1007/s00453-009-9334-z