Abstract
We will give distributed approximation schemes for the maximum matching problem and the minimum connected dominating set problem in unit-disk graphs. The algorithms are deterministic, run in a poly-logarithmic number of rounds in the message passing model and the approximation error can be made O(1/logk|G|) where |G| is the order of the graph and k is a positive integer.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Maximum Match
- Polynomial Time Approximation Scheme
- Unit Disk Graph
- Auxiliary Graph
- Message Passing Model
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Awerbuch, B., Goldberg, A.V., Luby, M., Plotkin, S.A.: Network Decomposition and Locality in Distributed Computation. In: Proc. 30th IEEE Symp. on Foundations of Computer Science, pp. 364–369 (1989)
Cheng, X., Huang, X., Li, D., Wu, W., Du, D.-Z.: Polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Networks 42(4), 202–208 (2003)
Czygrinow, A., Hańćkowiak, M.: Distributed algorithms for weighted problems in sparse graphs. Journal of Discrete Algorithms (in press, 2006)
Czygrinow, A., Hańćkowiak, M., Szymańska, E.: Distributed approximation algorithms for planar graphs. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006. LNCS, vol. 3998. Springer, Heidelberg (2006)
Diestel, R.: Graph Theory. Springer, New York (1997)
Dai, F., Wu, J.: An Extended Localized Algorithm for Connected Dominating Set Formation in Ad Hoc Wireless Networks. IEEE Transactions on Parallel and Distributed Systems 15(10), 908–920 (2004)
Dubhashi, D., Mei, A., Panconesi, A., Radhakrishnan, J., Srinivasan, A.: Fast Distributed Algorithms for (Weakly) Connected Dominating Sets and Linear-Size Skeletons. In: Proc. of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 717–724 (2003)
Gao, J., Guibas, L., Hershberger, J., Zhang, L., Zhu, A.: Discrete mobile centers. In: Proc of the 17th annual Symposium on Computational Geometry (SCG), pp. 188–196 (2001)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: On the Locality of Bounded Growth. In: 24th ACM Symposium on the Principles of Distributed Computing (PODC), Las Vegas, Nevada, USA, pp. 60–68 (2005)
Kuhn, F., Moscibroda, T., Nieberg, T., Wattenhofer, R.: Fast Deterministic Distributed Maximal Independent Set Computation on Growth-Bounded Graphs. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 273–287. Springer, Heidelberg (2005)
Kuhn, F., Moscibroda, T., Nieberg, T., Wattenhofer, R.: Local Approximation Schemes for Ad Hoc and Sensor Networks. In: 3rd ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), Cologne, Germany, pp. 97–103 (2005)
Lichtenstein, D.: Planar Formulae and Their Uses. SIAM Journal of Computing 11(2), 329–343 (1998)
Linial, N.: Locality in distributed graph algorithms. SIAM Journal on Computing 21(1), 193–201 (1992)
Nieberg, T., Hurink, J.L.: A PTAS for the Minimum Dominating Set Problem in Unit Disk Graphs. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 296–306. Springer, Heidelberg (2006)
Panconesi, A., Rizzi, R.: Some Simple Distributed Algorithms for Sparse Networks. Distributed Computing 14, 97–100 (2001)
Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Czygrinow, A., Hańćkowiak, M. (2006). Distributed Approximation Algorithms in Unit-Disk Graphs. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_27
Download citation
DOI: https://doi.org/10.1007/11864219_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44624-8
Online ISBN: 978-3-540-44627-9
eBook Packages: Computer ScienceComputer Science (R0)