Abstract
We will present an algorithm, based on SA-techniques and a sampling procedure, that colors a given random 3-colorable graph with high probability in sublinear time. This result is the first theoretical proof for the excellent experimental performance results of Simulated Annealing known from the literature when applied to graph coloring problems.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Alon, N.; Kahale, N.: A spectral technique for coloring random 3-colorable graphs, Proceedings of the 26th Symposium on Theory of Computing, 1994
Angluin, D.; Valiant, L.G.: Fast probabilistic algorithms for Hamiltonian circuits and matchings, Journal of Computer System Science 18, 1979
Blum, A.; Spencer, J.: Coloring Random and Semi-Random k-Colorable graphs, Journal of Algorithms 19, 1995
Chung, K.L.: Markov chains with stationary transition probabilities, Springer Verlag, Heidelberg, 1960.
Dyer, M.; Frieze, A.: The Solution of Some Random NP-Hard Problems in Polynomial Expected Time, Journal of Algorithms 10, 1989
Feller, W.: An introduction to probability theory and its applications, Volume 1, John Wiley & Sons, New York, 1950
Garey, M.R.; Johnson, S.J.: Computers and Intractability, W.H. Freeman and Company, 1979
Jensen, T.; Toft, B.: Graph Coloring Problems, John Wiley & Sons, 1995
Jerrum, J; Sorkin, G.: Simulated Annealing for Graph Bisection, Technical Report 1993, LFCS, University of Edinburgh
Johnson, D.S.; Aragon, C.R.; McGeoch, L.A.; Schevon, C.: Optimization by Simulated Annealing: An Experimental Evaluation, Operations Research 39, 1991
Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P.: Optimization by Simulated Annealing, Science 220, 1983.
Kucera, L.: Expected behaviour of graph coloring algorithms, Lecture Notes in Computer Science 56, 1977
Laarhoven, P.J.M.; Aarts, E.H.L.: Simulated Annealing: Theory and Applications, Kluwer Academic Publishers, 1989.
Lindvall, T.: Lectures on the Coupling method, John Wiley & Sons, 1992
Metropolis, N.; Rosenbluth, M.; Rosenbluth, M.; Teller, A.; Teller, E.: Equation of state calculations by fast computer machines, Journal of Chemical Physics 21, 1953
Petford, A.D.; Welsh, D.J.A.: A Randomized 3-Coloring Algorithm, Discrete Mathematics 74 (1989), North Holland
Sasaki, G.H.; Hajek, B.: The Time Complexity of Maximum Matching by Simulated Annealing, Journal of the Association for Computing Machinery 35, 1988
Turner, J.: Almost All k-Colorable Graphs Are Easy to Color, Journal of Algorithms 9, 1988
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nolte, A., Schrader, R. (1997). Coloring in sublinear time. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_30
Download citation
DOI: https://doi.org/10.1007/3-540-63397-9_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63397-6
Online ISBN: 978-3-540-69536-3
eBook Packages: Springer Book Archive