Abstract
We study the problem of the amount of information (advice) about a graph that must be given to its nodes in order to achieve fast distributed computations. The required size of the advice enables to measure the information sensitivity of a network problem. A problem is information sensitive if little advice is enough to solve the problem rapidly (i.e., much faster than in the absence of any advice), whereas it is information insensitive if it requires giving a lot of information to the nodes in order to ensure fast computation of the solution. In this paper, we study the information sensitivity of distributed graph coloring.
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., Babai, L., Itai, A.: A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem. J. Algorithms 7(4), 567–583 (1986)
Awerbuch, B., Goldberg, A., Luby, M., Plotkin, S.: Network Decomposition and Locality in Distributed Computation. In: 30th Symp. on Foundations of Computer Science(FOCS), pp. 364–369 (1989)
Bellare, M., Goldreich, O., Sudan, M.: Free Bits, PCPs, and Nonapproximability – Towards Tight Results. SIAM Journal on Computing 27(3), 804–915 (1998)
Cohen, R., Fraigniaud, P., Ilcinkas, D., Korman, A., Peleg, D.: Label-Guided Graph Exploration by a Finite Automaton. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 335–346. Springer, Heidelberg (2005)
Cohen, R., Fraigniaud, P., Ilcinkas, D., Korman, A., Peleg, D.: Labeling Schemes for Tree Representation. In: Pal, A., Kshemkalyani, A.D., Kumar, R., Gupta, A. (eds.) IWDC 2005. LNCS, vol. 3741, pp. 13–24. Springer, Heidelberg (2005)
Cole, R., Vishkin, U.: Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms. In: STOC. 18th ACM Symp. on Theory of Computing, pp. 206–219. ACM Press, New York (1986)
Feige, U., Kilian, J.: Zero Knowledge and the Chromatic Number. J. Comput. Syst. Sci. 57(2), 187–199 (1998)
Fich, F., Ruppert, E.: Hundreds of impossibility results for distributed computing. Distributed Computing 16, 121–163 (2003)
Fraigniaud, P., Ilcinkas, D., Pelc, A.: Oracle size: a new measure of difficulty for communication tasks. In: PODC. 25th ACM Symp. on Principles of Distributed Computing, pp. 179–187. ACM Press, New York (2006)
Goldberg, A., Plotkin, S.: Efficient parallel algorithms for (Δ + 1)-coloring and maximal independent set problems. In: STOC. 19th ACM Symp. on Theory of Computing, pp. 315–324. ACM Press, New York (1987)
Goldberg, A., Plotkin, S., Shannon, G.: Parallel symmetry-breaking in sparse graphs. In: STOC. 19th ACM Symp. on Theory of Computing, pp. 315–324. ACM Press, New York (1987)
Karp, R.: Reducibility Among Combinatorial Problems. Complexity of Computer Computations, 85–103 (1972)
Kothapalli, K., Onus, M., Scheideler, C., Schindelhauer, C.: Distributed coloring in \(O(\sqrt{\log n})\) bit rounds. In: 20th IEEE International Parallel and Distributed Processing Symposium (IPDPS), IEEE Computer Society Press, Los Alamitos (2006)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed Locally! In: PODC. 23th ACM Symp. on Principles of Distributed Computing, pp. 300–309. ACM Press, New York (2004)
Kuhn, F., Wattenhofer, R.: On the complexity of distributed graph coloring. In: PODC. 25th ACM Symp. on Principles of Distributed Computing, pp. 7–15. ACM Press, New York (2006)
Linial, N.: Locality in distributed graph algorithms. SIAM J. on Computing 21(1), 193–201 (1992)
Luby, M.: A Simple Parallel Algorithm for the Maximal Independent Set Problem. SIAM J. Comput. 15(4), 1036–1053 (1986)
Lynch, N.: A hundred impossibility proofs for distributed computing. In: PODC. 8th ACM Symp. on Principles of Distributed Computing, pp. 1–28. ACM Press, New York (1989)
Moscibroda, T., Wattenhofer, R.: Coloring unstructured radio networks. In: SPAA. 17th ACM Symp. on Parallelism in Algorithms and Architectures, pp. 39–48. ACM Press, New York (2005)
Naor, M., Stockmeyer, L.: What can be computed locally? In: STOC. 25th ACM Symposium on Theory of Computing, pp. 184–193. ACM Press, New York (1993)
Panconesi, A., Rizzi, R.: Some simple distributed algorithms for sparse networks. Distributed Computing 14, 97–100 (2001)
Panconesi, A., Srinivasan, A.: Improved distributed algorithms for coloring and network decomposition problems. In: STOC. 24th ACM Symp. on Theory of Computing, pp. 581–592. ACM Press, New York (1992)
Panconesi, A., Srinivasan, A.: On the complexity of distributed network decomposition. Journal of Algorithms 20(2), 356–374 (1996)
Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fraigniaud, P., Gavoille, C., Ilcinkas, D., Pelc, A. (2007). Distributed Computing with Advice: Information Sensitivity of Graph Coloring. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-73420-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73419-2
Online ISBN: 978-3-540-73420-8
eBook Packages: Computer ScienceComputer Science (R0)