Abstract
In this paper we prove explicit lower bounds on the approximability of some graph problems restricted to instances which are already colored with a constant number of colors. As far as we know, this is the first time these problems are explicitily defined and analyzed. This allows us to drastically improve the previously known inapproximability results which were mainly a consequence of the analysis of bounded-degree graph problems. Moreover, we apply one of these results to obtain new lower bounds on the approximabiluty of the minimum delay schedule problem on store-and-forward networks of bounded diameter. Finally, we propose a generalization of our analysis of the complexity of approximating colored-graph problems to the complexity of approximating approximated optimization problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Feige, U., Wigderson, A., And Zuckerman, D. Derandomized graph products. Computational Complexity 5 (1995), 60–75.
Appel, K., And Haken, W. Every planar map is four colorable. part I: discharging. Illinois J. Math. 21 (1977), 429–490.
Appel, K., And Haken, W. Every planar map is four colorable. part II: reducibility. Illinois J. Math. 21 (1977), 491–567.
Berman, P., And Karpinski, M. On some tighter inapproximability results. Further improvements. Tech. Rep. TR98-065, ECCC, 1998.
Boppana, R., And HalldÓrsson, M. M. Approximating maximum independent sets by excluding subgraphs. Bit 32 (1992), 180–196.
Clementi, A., And Di Ianni, M. On the hardness of approximating optimum schedule problems in store and forward networks. IEEE/ACM Transaction on Networking 4 (1996), 272–280.
Feige, U., And Kilian, J. Zero knowledge and the chromatic number. In Proc. Eleventh Ann. IEEE Conf. on Comp. Complexity (1996), IEEE Computer Society, pp. 278–287.
Garey, M., Johnson, D., And Stockmeyer, L. Some simplified NP-complete graph problems. Theoretical Comput. Sci. 1 (1976), 237–267.
Garey, M. R., AND Johnson, D. S.Computers and Intractability: a guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco, 1979.
Goemans, M. X., AND Williamson, D. P. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42 (1995b), 1115–1145.
HalldÓrsson, M. M. A still better performance guarantee for approximate graph coloring. Inform. Process. Lett. 45 (1993a), 19–23.
HÅstad, J. Clique is hard to approximate within n1 − ∈. In Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci. (1996), IEEE Computer Society, pp. 627–636.
HÅstad, J. Some optimal inapproximability results. In Proc. 29th Ann. ACM Symp. on Theory of Comp. (1997), ACM, pp. 1–10.
Hochbaum, D. S. Efficient bounds for the stable set, vertex cover and set packing problems. Disc. Appl. Math. 6 (1983), 243–254.
Karger, D., Motwani, R., AND Sudan, M. Approximate graph coloring by semidefinite programming. J. ACM 45 (1998), 246–265.
Khanna, S., Linial, N., AND Safra, S. On the hardness of approximating the chromatic number. In Proc. 1st Israel Symp. on Theory of Computing and Systems (1992), IEEE Computer Society, pp. 250–260.
Leighton, F.Introduction to parallel algorithms and architectures: arrays, trees, hypercubes. Morgan Kaufmann, San Mateo, CA, 1992.
Lovasz, L. Three short proofs in graph theory. J. Combin. Theory 19 (1975), 269–271.
Monien, B., AND Speckenmeyer, E. Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Inf. 22 (1985), 115–123.
Papadimitriou, C. H., AND Yannakakis, M. Optimization, approximation, and complexity classes. J. Comput. System Sci. 43 (1991), 425–440.
Trevisan, L. Approximating satisfiable satisfiability problems. In Proc. 5th Ann. European Symp. on Algorithms (1997), Springer-Verlag, pp. 472–485.
Zwick, U. Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint. In Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms (1998), ACM-SIAM, p. 201.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clementi, A.E.F., Crescenzi, P., Rossi, G. (1999). On the Complexity of Approximating Colored-Graph Problems Extended Abstract. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_28
Download citation
DOI: https://doi.org/10.1007/3-540-48686-0_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66200-6
Online ISBN: 978-3-540-48686-2
eBook Packages: Springer Book Archive