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Optimal Gossiping in Directed Geometric Radio Networks in Presence of Dynamical Faults

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Mathematical Foundations of Computer Science 2007 (MFCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4708))

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Abstract

We study deterministic fault-tolerant gossiping protocols in directed Geometric Radio Networks (in short, directed GRN). Unpredictable node and link faults may happen during every time slot of the protocol’s execution.

We first consider the single-message model where every node can send at most one message per time slot. We provide a protocol that, in any directed GRN G of n nodes, completes gossiping in O(n Δ) time (where Δ is the maximal in-degree of G) and has message complexity O(n 2). Both bounds are then shown to be optimal.

As for the combined-message model, we give a protocol working in optimal completion time O(DΔ) (where D is the maximal source eccentricity) and message complexity O(Dn). Finally, our protocol performs the (single) broadcast operation within the same optimal time and optimal message complexity O(n).

Research partially supported by the EU under the EU/IST Project 15964 AEOLUS.

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References

  1. Adler, M., Scheideler, C.: Efficient communication strategies for ad hoc wireless networks. In: Proc. of 10th ACM SPAA, pp. 259–268 (1998)

    Google Scholar 

  2. Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. Journal of Computer and System Science 43, 290–298 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  3. Awerbuch, B., Berenbrink, P., Brinkmann, A., Scheideler, C.: Simple routing strategies for adversarial systems. In: Proc. of 42th IEEE FOCS, pp. 158–167 (2001)

    Google Scholar 

  4. Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization. Journal of Computer and System Science 45, 104–126 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bar-Yehuda, R., Israeli, A., Itai, A.: Multiple communication in multi-hop radio networks. SICOMP 22(4), 875–887 (1993)

    MATH  MathSciNet  Google Scholar 

  6. Calamoneri, T.: The L(h,k)-Labeling problem: Survey and Annotated Bibliography. The Computer Journal 49, 585–608 (2006)

    Article  Google Scholar 

  7. Calinescu, G., Kapoor, S., Olshevsky, A., Zelikovsky, A.: Network Life Time and Power Assignment in ad hoc Wireless Networks. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 114–126. Springer, Heidelberg (2003)

    Google Scholar 

  8. Chlebus, B., Gasieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. In: Proc. of 11th ACM-SIAM SODA, pp. 861–870 (2000)

    Google Scholar 

  9. Chrobak, M., Gasieniec, L., Rytter, W.: Fast Broadcasting and Gossiping in Radio Networks. Journal of Algorithms 43(2), 177–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Mathematics 86, 165–177 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Clementi, A.E.F., Crescenzi, P., Penna, P., Vocca, P.: On the complexity of minimum energy consumption broadcast subgraphs. In: Proc of 11th STACS, pp. 121–131 (2001)

    Google Scholar 

  12. Clementi, A.E.F., Monti, A., Silvestri, R.: Distributed broadcast in radio networks of unknown topology. Theoretical Computer Science 302, 337–364 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Clementi, A.E.F., Monti, A., Silvestri, R.: Round Robin is optimal for fault-tolerant broadcasting on wireless networks. Journal of Parallel and Distributed Computing 64(1), 89–96 (2004)

    Article  MATH  Google Scholar 

  14. Clementi, A.E.F., Monti, A., Pasquale, F., Silvestri, R.: Optimal gossiping in directed geometric radio networks in presence of dynamical faults (2007), available at www.mat.uniroma2.it/~pasquale

  15. Clementi, A.E.F., Penna, P., Silvestri, R.: On the power assignment problem in radio networks. MONET (9), 125–140 (2004)

    Google Scholar 

  16. Czumaj, A., Rytter, W.: Broadcasting algorithms in radio networks with unknown topology. Journal of Algorithms 60(2), 115–143 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. Ephremides, A., Nguyen, G., Wieselthier, J.: On the construction of energy-efficient broadcast and multi-cast trees in wireless networks. In: Proc. of 19th IEEE INFOCOM, pp. 585–594 (2000)

    Google Scholar 

  19. Gasieniec, L., Lingas, A.: On adaptive deterministic gossiping in ad-hoc radio networks. Information Processing Letters 2, 89–93 (2002)

    Article  MathSciNet  Google Scholar 

  20. Gasieniec, L., Peleg, D., Xin, Q.: Faster Communication in Known Topology Radio Networks. In: Proc. of 24th ACM PODC, pp. 129–137 (2005)

    Google Scholar 

  21. Indyk, P.: Deterministic Superimposed Coding with Application to Pattern Matching. In: Proc. of 38th IEEE FOCS, pp. 127–136 (1997)

    Google Scholar 

  22. Indyk, P.: Explicit constructions of selectors and related combinatorial structures, with applications. In: Proc of 13th ACM-SIAM SODA, pp. 697–704 (2002)

    Google Scholar 

  23. Kirousis, L., Kranakis, E., Krizanc, D., Pelc, A.: Power consumption in packet radio networks. Theoretical Computer Science 243, 289–305 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kranakis, E., Krizanc, D., Pelc, A.: Fault-Tolerant Broadcasting in Radio Networks. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 283–294. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  25. Pelc, A.: Broadcasting in radio networks. In: Handbook of Wireless Networks and Mobile Computing, pp. 509–528. John Wiley and Sons, Inc., Chichester (2002)

    Chapter  Google Scholar 

  26. Pelc, A., Peleg, D.: Feasibility and complexity of broadcasting with random transmission failures. In: Proc. of 24th ACM PODC, pp. 334–341 (2005)

    Google Scholar 

  27. Pagani, E., Rossi, G.: Reliable Broadcast in Mobile Multihop Packet Networks. In: Proc. of 3rd ACM-IEEE MOBICOM, pp. 34–42 (1997)

    Google Scholar 

  28. Rappaport, T.S.: Wireless Communications: Principles and Practice. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

  29. Sen, A., Malesinska, E.: On Approximation algorithms for packet radio scheduling. In: Proc. of 35th Allerton Conference on Communication, Control and Computing, Allerton, pp. 573–582 (1997)

    Google Scholar 

  30. Scheideler, C.: Models and Techniques for Communication in Dynamic Networks. In: Proc. of 18th STACS, pp. 27–49 (2001)

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”,  

    Andrea E. F. Clementi & Francesco Pasquale

  2. Dipartimento di Informatica, Università di Roma “La Sapienza”,  

    Angelo Monti & Riccardo Silvestri

Authors
  1. Andrea E. F. Clementi
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  2. Angelo Monti
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  3. Francesco Pasquale
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  4. Riccardo Silvestri
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Luděk Kučera Antonín Kučera

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Clementi, A.E.F., Monti, A., Pasquale, F., Silvestri, R. (2007). Optimal Gossiping in Directed Geometric Radio Networks in Presence of Dynamical Faults. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_39

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  • DOI: https://doi.org/10.1007/978-3-540-74456-6_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74455-9

  • Online ISBN: 978-3-540-74456-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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