Article

Fast Distributed Approximations in Planar Graphs

Authors:

Andrzej Czygrinow,

Michal Hańćkowiak,

Wojciech WawrzyniakAuthors Info & Claims

DISC '08: Proceedings of the 22nd international symposium on Distributed Computing

Pages 78 - 92

https://doi.org/10.1007/978-3-540-87779-0_6

Published: 22 September 2008 Publication History

Abstract

We give deterministic distributed algorithms that given ï > 0 find in a planar graph G , (1± ï )-approximations of a maximum independent set, a maximum matching, and a minimum dominating set. The algorithms run in O (log^*| G |) rounds. In addition, we prove that no faster deterministic approximation is possible and show that if randomization is allowed it is possible to beat the lower bound for deterministic algorithms.

References

[1]

Beauquier, J., Debas, O.: An optimal self-stabilizing algorithm for mutual exclusion on bidirectional non uniform rings. Proceedings of the Second Workshop on Self-Stabilizing Systems 13, 17.1-17.13 (1995).

[2]

Burns, J.E., Gouda, M.G., Miller, R.E.: On relaxing interleaving assumptions. In: Proceedings of the MCC Workshop on Self-Stabilizing Systems, MCC Technical Report No. STP-379-89 (1989).

[3]

Beauquier, J., Johnen, C., Messika, S.: Brief announcement: Computing automatically the stabilization time against the worst and the best schedules. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 543-547. Springer, Heidelberg (2006).

[4]

Cobb, J.A., Gouda, M.G.: Stabilization of general loop-free routing. Journal of Parallel and Distributed Computing 62(5), 922-944 (2002).

Digital Library

[5]

Chang, E.J.H., Gonnet, G.H., Rotem, D.: On the costs of self-stabilization. Information Processing Letters 24, 311-316 (1987).

Digital Library

[6]

Chernoy, V., Shalom, M., Zaks, S.: On the performance of Dijkstra's third self-stabilizing algorithm for mutual exclusion. In: 9th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Paris, November 2007, pp. 114-123 (2007).

Digital Library

[7]

Chernoy, V., Shalom, M., Zaks, S.: On the performance of Beauquier and Debas' self-stabilizing algorithm for mutual exclusion. In: Shvartsman, M.M.A.A., Felber, P. (eds.) SIROCCO 2008. LNCS, vol. 5058, pp. 221-233. Springer, Heidelberg (2008).

[8]

Chernoy, V., Shalom, M., Zaks, S.: A self-stabilizing algorithm with tight bounds for mutual exclusion on a ring. Technical Report CS-2008-09, Department of Computer Science, Technion, Haifa, Israel (July 2008).

[9]

Dijkstra, E.W.: Self stabilizing systems in spite of distributed control. Communications of the Association of the ComputingMachinery 17(11), 643-644 (1974).

[10]

Dijkstra, E.W.: A belated proof of self-stabilization. Distributed Computing 1, 5-6 (1986).

Digital Library

[11]

Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000).

[12]

Kessels, J.L.W.: An exercise in proving self-stabilization with a variant function. Information Processing Letters 29, 39-42 (1988).

Digital Library

[13]

Kruijer, H.S.M.: Self-stabilization (in spite of distributed control) in tree-structured systems. Information Processing Letters 8, 91-95 (1979).

[14]

Nakaminami, Y., Kakugawa, H., Masuzawa, T.: An advanced performance analysis of self-stabilizing protocols: stabilization time with transient faults during convergence. In: 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Rhodes Island, Greece, April 25-29 (2006).

Digital Library

[15]

Tsuchiya, T., Tokuda, Y., Kikuno, T.: Computing the stabilization times of self-stabilizing systems. IEICE Transactions on Fundamentals of Electronic Communications and Computer Sciences E83A(11), 2245-2252 (2000).

Cited By

Chang YOshman RNolin AHalldorsson MBalliu A(2023)Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their ApplicationsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594604(55-66)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594604
Agrawal AAugustine JPeleg DRamachandran SOshman RNolin AHalldorsson MBalliu A(2023)Brief Announcement: Local Problems in the SUPPORTED ModelProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594583(172-175)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594583
Chang YLi ZOshman RNolin AHalldorsson MBalliu A(2023)The Complexity of Distributed Approximation of Packing and Covering Integer Linear ProgramsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594562(32-43)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594562
Show More Cited By

Index Terms

Fast Distributed Approximations in Planar Graphs
1. Mathematics of computing
2. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

Recommendations

Distributed Dominating Set Approximations beyond Planar Graphs

The Minimum Dominating Set (MDS) problem is a fundamental and challenging problem in distributed computing. While it is well known that minimum dominating sets cannot be well approximated locally on general graphs, in recent years there has been much ...
Fast distributed coloring algorithms for triangle-free graphs
ICALP'13: Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II

Vertex coloring is a central concept in graph theory and an important symmetry-breaking primitive in distributed computing. Whereas degree-Δ graphs may require palettes of Δ+1 colors in the worst case, it is well known that the chromatic number of many ...
Distributed Algorithms for Planar Networks I: Planar Embedding
PODC '16: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing

This paper presents the first (non-trivial) distributed planar embedding algorithm. We consider this a crucial first step in a broader program to design efficient distributed algorithms for planar networks. We work in the standard distributed model in ...

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

DISC '08: Proceedings of the 22nd international symposium on Distributed Computing

September 2008

519 pages

ISBN:9783540877783

Editor:
Gadi Taubenfeld

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 22 September 2008

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

49
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 12 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

Chang YOshman RNolin AHalldorsson MBalliu A(2023)Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their ApplicationsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594604(55-66)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594604
Agrawal AAugustine JPeleg DRamachandran SOshman RNolin AHalldorsson MBalliu A(2023)Brief Announcement: Local Problems in the SUPPORTED ModelProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594583(172-175)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594583
Chang YLi ZOshman RNolin AHalldorsson MBalliu A(2023)The Complexity of Distributed Approximation of Packing and Covering Integer Linear ProgramsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594562(32-43)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594562
Chang Y(2023)The Energy Complexity of Diameter and Minimum Cut Computation in Bounded-Genus NetworksStructural Information and Communication Complexity10.1007/978-3-031-32733-9_12(262-296)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-32733-9_12
Coy SCzumaj ALeonardi SGupta A(2022)Deterministic massively parallel connectivityProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520055(162-175)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520055
Dory MGhaffari MIlchi SMilani AWoelfel P(2022)Near-Optimal Distributed Dominating Set in Bounded Arboricity GraphsProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538437(292-300)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538437
Chang YSu HMilani AWoelfel P(2022)Narrowing the LOCAL-CONGEST Gaps in Sparse Networks via Expander DecompositionsProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538423(301-312)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538423
Konrad CZamaraev V(2022)Distributed minimum vertex coloring and maximum independent set in chordal graphsTheoretical Computer Science10.1016/j.tcs.2022.04.047922:C(486-502)Online publication date: 24-Jun-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.04.047
Abboud ACensor-Hillel KKhoury SPaz A(2021)Smaller Cuts, Higher Lower BoundsACM Transactions on Algorithms10.1145/346983417:4(1-40)Online publication date: 4-Oct-2021
https://dl.acm.org/doi/10.1145/3469834
Kublenz SSiebertz SVigny A(2021)Constant Round Distributed Domination on Graph Classes with Bounded ExpansionStructural Information and Communication Complexity10.1007/978-3-030-79527-6_19(334-351)Online publication date: 28-Jun-2021
https://dl.acm.org/doi/10.1007/978-3-030-79527-6_19
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Table of Contents