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Trade-offs Between the Size of Advice and Broadcasting Time in Trees

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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 O(n ε), for an arbitrarily small positive constant ε. This is the first communication problem for which a trade-off between the size of advice and the efficiency of the solution is shown for arbitrary size of advice.

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References

  1. Abiteboul, S., Kaplan, H., Milo, T.: Compact labeling schemes for ancestor queries. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 547–556

  2. Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. J. Comput. Syst. Sci. 43, 290–298 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Awerbuch, B., Goldreich, O., Peleg, D., Vainish, R.: A tradeoff between information and communication in broadcast protocols. J. ACM 37, 238–256 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bender, M.A., Fernandez, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: Exploring and mapping directed graphs. Inf. Comput. 176, 1–21 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chierichetti, F.: Personal communication (2009)

  6. Clementi, A.E.F., Monti, A., Silvestri, R.: Selective families, superimposed codes, and broadcasting on unknown radio networks. In: Proc. 12th Ann. ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 709–718

  7. Cohen, R., Fraigniaud, P., Ilcinkas, D., Korman, A., Peleg, D.: Label-guided graph exploration by a finite automaton. In: Proc. 32th International Colloquium on Automata, Languages and Programming (ICALP 2005). LNCS, vol. 3580, pp. 335–346

  8. Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. In: Proc. 44th Symp. on Foundations of Computer Science (FOCS 2003), pp. 492–501

  9. Dessmark, A., Pelc, A.: Optimal graph exploration without good maps. Theor. Comput. Sci. 326, 343–362 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dessmark, A., Pelc, A.: Broadcasting in geometric radio networks. J. Discrete Algorithms 5, 187–201 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Diks, K., Kranakis, E., Krizanc, D., Pelc, A.: The impact of knowledge on broadcasting time in linear radio networks. Theor. Comput. Sci. 287, 449–471 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Elkin, M., Kortsarz, G.: A sublogarithmic approximation algorithm for the undirected telephone broadcast problem: a path out of a jungle. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 76–85

  13. Fich, F., Ruppert, E.: Hundreds of impossibility results for distributed computing. Distributed Comput. 16, 121–163 (2003)

    Article  Google Scholar 

  14. Fraigniaud, P., Gavoille, C., Ilcinkas, D., Pelc, A.: Distributed computing with advice: information sensitivity of graph coloring. In: Proc. 34th International Colloquium on Automata, Languages and Programming (ICALP 2007). LNCS, vol. 4596, pp. 231–242

  15. Fraigniaud, P., Ilcinkas, D., Pelc, A.: Oracle size: a new measure of difficulty for communication problems. In: Proc. 25th Ann. ACM Symposium on Principles of Distributed Computing (PODC 2006), pp. 179–187

  16. Fraigniaud, P., Ilcinkas, D., Pelc, A.: Tree exploration with an oracle. In: Proc. 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006). LNCS, vol. 4162, pp. 24–37

  17. Fraigniaud, P., Korman, A., Lebhar, E.: Local MST computation with short advice. In: Proc. 19th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2007), pp. 154–160

  18. Gavoille, C., Peleg, D., Pérennes, S., Raz, R.: Distance labeling in graphs. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 210–219

  19. Ilcinkas, D., Kowalski, D., Pelc, A.: Fast radio broadcasting with advice. In: Proc. 15th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2008). LNCS, vol. 5058, pp. 291–305

  20. Katz, M., Katz, N., Korman, A., Peleg, D.: Labeling schemes for flow and connectivity. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 927–936

  21. Korman, A., Kutten, S., Peleg, D.: Proof labeling schemes. In: Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC 2005), pp. 9–18

  22. Kortsarz, G., Peleg, D.: Approximation algorithms for minimum time broadcast. SIAM J. Discrete Math. 8, 401–427 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kowalski, D., Pelc, A.: Broadcasting in undirected ad hoc radio networks. Distrib. Comput. 18, 43–57 (2005)

    Article  Google Scholar 

  24. Kowalski, D., Pelc, A.: Optimal deterministic broadcasting in known topology radio networks. Distrib. Comput. 19, 185–195 (2007)

    Article  Google Scholar 

  25. Lynch, N.: A hundred impossibility proofs for distributed computing. In: Proceedings of the 8th Annual ACM Symposium on Principles of Distributed Computing (PODC 1989), pp. 1–28

  26. Pelc, A.: Activating anonymous ad hoc radio networks. Distrib. Comput. 19, 361–371 (2007)

    Article  Google Scholar 

  27. Proskurowski, A.: Minimum broadcast trees. IEEE Trans. Comput. C-30(5), 363–366 (1981)

    Article  Google Scholar 

  28. Slater, P.J., Cockayne, E.J., Hedetniemi, S.T.: Information dissemination in trees. SIAM J. Comput. 10, 692–701 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  29. Soguet, D., Nisse, N.: Graph searching with advice. In: Proc. 14th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2007). LNCS, vol. 4474, pp. 51–65

  30. Thorup, M., Zwick, U.: Approximate distance oracles. J. ACM 52(1), 1–24 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, University of Rome “La Sapienza”, 00198, Rome, Italy

    Emanuele G. Fusco

  2. Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec, J8X 3X7, Canada

    Andrzej Pelc

Authors
  1. Emanuele G. Fusco
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  2. Andrzej Pelc
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Correspondence to Emanuele G. Fusco.

Additional information

A preliminary version of this paper appeared in the Proc. of the 20th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2008).

This work was done during the visit of Emanuele G. Fusco at the Research Chair in Distributed Computing of the Université du Québec en Outaouais.

A. Pelc was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais.

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Fusco, E.G., Pelc, A. Trade-offs Between the Size of Advice and Broadcasting Time in Trees. Algorithmica 60, 719–734 (2011). https://doi.org/10.1007/s00453-009-9361-9

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