skip to main content
10.1145/1378533.1378545acmconferencesArticle/Chapter ViewAbstractPublication PagesspaaConference Proceedingsconference-collections
research-article

Trade-offs between the size of advice and broadcasting time in trees

Published: 14 June 2008 Publication History

Abstract

We study the problem of the amount of information required to perform fast broadcasting in tree networks. The source located at the root of a tree has to disseminate a message to all nodes. In each round each informed node can transmit to one child. Nodes do not know the topology of the tree but an oracle knowing it can give a string of bits of advice to the source which can then pass it down the tree with the source message. The quality of a broadcasting algorithm with advice is measured by its competitive ratio: the worst case ratio, taken over n-node trees, between the time of this algorithm and the optimal broadcasting time in the given tree. Our goal is to find a trade-off between the size of advice and the best competitive ratio of a broadcasting algorithm for n-node trees. We establish such a trade-off with an approximation factor of Onε), for an arbitrarily small positive constant ε. This is the first problem for which a trade-off between the amount of provided information and the efficiency of the solution is shown for arbitrary size of advice.

References

[1]
S. Abiteboul, H. Kaplan, and T. Milo. Compact labeling schemes for ancestor queries. In SODA'01: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, pages 547--556, Philadelphia, PA, USA, 2001. Society for Industrial and Applied Mathematics.
[2]
N. Alon, A. Bar-Noy, N. Linial, and D. Peleg. A lower bound for radio broadcast. J. Comput. Syst. Sci., 43(2):290--298, 1991.
[3]
B. Awerbuch, O. Goldreich, R. Vainish, and D. Peleg. A trade-off between information and communication in broadcast protocols. J. ACM, 37(2):238--256, 1990.
[4]
M. A. Bender, A. Fernández, D. Ron, A. Sahai, and S. Vadhan. The power of a pebble: Exploring and mapping directed graphs. Information and Computation, 176:1--21, 2002.
[5]
A. E. F. Clementi, A. Monti, and R. Silvestri. Selective families, superimposed codes, and broadcasting on unknown radio networks. In SODA'01: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, pages 709--718, Philadelphia, PA, USA, 2001. Society for Industrial and Applied Mathematics.
[6]
A. Czumaj and W. Rytter. Broadcasting algorithms in radio networks with unknown topology. J. Algorithms, 60(2):115--143, 2006.
[7]
A. Dessmark and A. Pelc. Optimal graph exploration without good maps. Theor. Comput. Sci., 326(1-3):343--362, 2004.
[8]
A. Dessmark and A. Pelc. Broadcasting in geometric radio networks. J. of Discrete Algorithms, 5(1):187--201, 2007.
[9]
K. Diks, E. Kranakis, D. Krizanc, and A. Pelc. The impact of knowledge on broadcasting time in linear radio networks. Theoretical Computer Science, 287:449--471, 2002.
[10]
M. Elkin and G. Kortsarz. A sublogarithmic approximation algorithm for the undirected telephone broadcast problem: a path out of a jungle. In SODA'03: Proceedings of the fourteenth ACM-SIAM Symposium on Discrete Algorithms, pages 76--85, 2003.
[11]
F. Fich and E. Ruppert. Hundreds of impossibility results for distributed computing. Distrib. Comput., 16(2-3):121--163, 2003.
[12]
P. Fraigniaud, C. Gavoille, D. Ilcinkas, and A. Pelc. Distributed computing with advice: Information sensitivity of graph coloring. In L. Arge, C. Cachin, T. Jurdzinski, and A. Tarlecki, editors, ICALP, volume 4596 of Lecture Notes in Computer Science, pages 231--242. Springer, 2007.
[13]
P. Fraigniaud, D. Ilcinkas, and A. Pelc. Oracle size: a new measure of difficulty for communication tasks. In PODC'06: Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing, pages 179--187, New York, NY, USA, 2006. ACM.
[14]
P. Fraigniaud, D. Ilcinkas, and A. Pelc. Tree exploration with an oracle. In Rastislav Kralovic and Pawel Urzyczyn, editors, MFCS, volume 4162 of Lecture Notes in Computer Science, pages 24--37. Springer, 2006.
[15]
P. Fraigniaud, A. Korman, and E. Lebhar. Local mst computation with short advice. In SPAA'07: Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures, pages 154--160, New York, NY, USA, 2007. ACM.
[16]
C. Gavoille, D. Peleg, S. Pérennes, and R. Raz. Distance labeling in graphs. InSODA'01: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, pages 210--219, Philadelphia, PA, USA, 2001. Society for Industrial and Applied Mathematics.
[17]
M. Katz, N. A. Katz, A. Korman, and D. Peleg. Labeling schemes for flow and connectivity. In SODA'02: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, pages 927--936, Philadelphia, PA, USA, 2002. Society for Industrial and Applied Mathematics.
[18]
A. Korman, S. Kutten, and D. Peleg. Proof labeling schemes. In PODC'05: Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing, pages 9--18, New York, NY, USA, 2005. ACM.
[19]
G. Kortsarz and D. Peleg. Approximation algorithms for minimum-time broadcast. SIAM J. Discret. Math., 8(3):401--427, 1995.
[20]
D. R. Kowalski and A. Pelc. Broadcasting in undirected ad hoc radio networks. Distrib. Comput., 18(1):43--57, 2005.
[21]
D. R. Kowalski and A. Pelc. Optimal deterministic broadcasting in known topology radio networks. Distributed Computing, 19(3):185--195, 2007.
[22]
N. Lynch. A hundred impossibility proofs for distributed computing. In Proceedings of the 8th ACM Symposium on Principles of Distributed Computing (PODC), pages 1--28, New York, NY, 1989. ACM Press.
[23]
N. Nisse and D. Soguet. Graph searching with advice. In G. Prencipe and S. Zaks, editors, SIROCCO, volume 4474 of Lecture Notes in Computer Science, pages 51--65. Springer, 2007.
[24]
A. Pelc. Activating anonymous ad hoc radio networks. Distributed Computing, 19(5-6):361--371, 2007.
[25]
A. Proskurowski. Minimum broadcast trees. IEEE Trans. Comput., 30(5):363--366, 1981.
[26]
P.J. Slater, E. J. Cockayne, and S. T. Hedetniemi. Information dissemination in trees. SIAM J. Comput., 10(4):692--701, 1981.
[27]
M. Thorup and U. Zwick. Approximate distance oracles. J. ACM, 52(1):1--24, 2005.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SPAA '08: Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
June 2008
380 pages
ISBN:9781595939739
DOI:10.1145/1378533
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 June 2008

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. advice
  2. broadcast
  3. tree

Qualifiers

  • Research-article

Conference

SPAA08

Acceptance Rates

Overall Acceptance Rate 447 of 1,461 submissions, 31%

Upcoming Conference

SPAA '25
37th ACM Symposium on Parallelism in Algorithms and Architectures
July 28 - August 1, 2025
Portland , OR , USA

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)2
  • Downloads (Last 6 weeks)0
Reflects downloads up to 19 Feb 2025

Other Metrics

Citations

Cited By

View all

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media