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Lower Bounds for Oblivious Single-Packet End-to-End Communication

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Distributed Computing (DISC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2848))

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Abstract

The end-to-end communication problem is a protocol design problem, for sending a packet from a specified source-node s to a specified target-node t, through an unreliable asynchronous communication network G. The protocol must insure reception and termination. In this paper, we measure the complexity of the protocol in term of header size, i.e., the quantity of information that must be attached to the packets to insure their delivery. We show that headers of Ω(log log τ) bits are required in every network, where τ denotes the tree-width of the network. In planar networks, Ω(log τ) bits are required. In particular, this latter lower bound closes the open problem by Adler and Fich in PODC ‘99 about the optimality of the hop-count protocol in square meshes.

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References

  1. Adler, M., Fich, F.: The Complexity of End-to-End Communication in Memory-less Networks. In: 18th ACM Symposium on Principles of Distributed Computing (PODC), pp. 239–248 (1999)

    Google Scholar 

  2. Adler, M., Fich, F., Goldberg, L., Paterson, M.: Tight Size Bounds for Packet Headers in Narrow Meshes. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 756–767. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Afek, Y., Awerbuch, B., Gaftii, E.: Applying Static Network Protocols to Dynamic Networks. In: 28th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 358–370 (1987)

    Google Scholar 

  4. Afek, Y., Gafni, E.: End-to-End Communication in Unreliable Networks. In: 7th ACM Symposium on Principles of Distributed Computing (PODC), pp. 131–148 (1988)

    Google Scholar 

  5. Afek, Y., Gafni, E.: Bootstrap Network Resynchonization. In: 10th ACM Symposium on Principles of Distributed Computing (PODC), pp. 295–307 (1991)

    Google Scholar 

  6. Afek, Y., Attiya, H., Fekete, A., Fischer, M., Lynch, N., Mansour, Y., Wang, D.-W., Zuck, L.: Reliable Communication Over Unreliable Channels. Journal of the ACM 41(6), 1267–1297 (1994)

    Article  MathSciNet  Google Scholar 

  7. Afek, Y., Awerbuch, B., Gafni, E., Mansour, Y., Rosén, A., Shavit, N.: Slide-The Key to Polynomial End-to-End Communication. Journal of Algorithms 22(1), 158–186 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Aho, A., Ullman, J., Wyler, A., Yannakakis, M.: Bounds on the Size and Transmission Rate of Communication Protocols. Computers and Math with Applications 8(3), 205–214 (1982)

    Article  MATH  Google Scholar 

  9. Amir, E.: Efficient approximation for triangulation of minimum treewidth. In: 17th Conference on Uncertainty in Artificial Intelligence, UAI (2001)

    Google Scholar 

  10. Arnborg, S.: Efficient Algorithms for Combinatorial Problems on Graphs with Bounded Decomposability-A Survey. BIT 25, 2–23 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  11. Arnborg, S., Corneil, D., Proskurowski, A.: Complexity of Finding Embeddings in a fc-Tree. SIAM J. Alg. Disc. Meth. 8, 277–284 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  12. Awerbuch, B., Even, S.: Reliable Broadcast Protocols in Unreliable Networks. Networks 16, 381–396 (1986)

    Article  Google Scholar 

  13. Awerbuch, B., Mansour, Y., Shavit, N.: Polynomial End-to-End Communication. In: 30th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 358–363 (1989)

    Google Scholar 

  14. Awerbuch, B., Goldreich, O., Herzberg, A.: A Quantitative Approach to Dynamic Networks. In: 9th ACM Symposium on Principles of Distributed Computing (PODC), pp. 189–203 (1990)

    Google Scholar 

  15. Bartlett, K., Scantleburg, R., Wilkinson, P.: A Note on Reliable, Full-Duplex Transmission over Half-Duplex Links. Communication of the ACM 12, 260–261 (1969)

    Article  Google Scholar 

  16. Bodlaender, H.: A Tourist Guide through Treewidth. Acta Cybernetica 11, 1–21 (1993)

    MATH  MathSciNet  Google Scholar 

  17. Bodlaender, H.: A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Bodlaender, H., Gilbert, J., Hafsteinsson, H., Kloks, T.: Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree. Journal of Algorithms 18, 238–255 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bouchitté, V., Kratsch, D., Müller, H., Todinca, I.: On treewidth approximations. In: 1st Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW (2001)

    Google Scholar 

  20. Diestel, R.: Graph Theory, 2nd edn. Springer, New York (2000)

    Google Scholar 

  21. Diestel, R., Jensen, T.R., Gorbunov, K.Y., Thomassen, C.: Highly connected sets and the excluded grid theorem. Journal of Combin. Theory B 75, 61–73 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  22. Dolev, S., Welch, J.: Crash Resilient Communication in Dynamic Networks. IEEE Transactions on Computers 46(1), 14–26 (1997)

    Article  Google Scholar 

  23. Fekete, A., Lynch, N.: The Need for Headers: An Impossibility Result for Communication over Unreliable Channels. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 199–215. Springer, Heidelberg (1990)

    Google Scholar 

  24. Fekete, A., Lynch, N., Mansour, Y., Spinelli, J.: The Impossibility of Implementing Reliable Communication in the Face of Crashes. Journal of the ACM 40(3), 1087–1107 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  25. Fich, F.: End-to-End Communication Protocols. In: 2nd Int. Conference on Principles of Distributed Systems (OPODIS), Hermes, pp. 37–43 (1998)

    Google Scholar 

  26. Fich, F., Jakoby, A.: Short Headers Suffice for Communication in a DAG with Link Failures. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 360–373. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  27. Goldreich, O., Herzberg, A., Mansour, Y.: Source to Destination Communication in the Presence of Faults. In: 8th ACM Symposium on Principles of Distributed Computing (PODC), pp. 85–101 (1989)

    Google Scholar 

  28. Herzberg, A.: Connection-Based Communication in Dynamic Networks. In: 11th ACM Symposium on Principles of Distributed Computing (PODC), pp. 13–24 (1992)

    Google Scholar 

  29. Kushilevitz, E., Ostrovsky, R., Rosén, A.: Log-Space Polynomial End-to-End Communication. In: 28th ACM Symposium on Theory of Computing (STOC), pp. 559–568 (1995)

    Google Scholar 

  30. Ladner, R., LaMarca, A., Tempero, E.: Counting Protocol for Reliable End-to-End Transmission. Journal of Computer and System Sciences 56, 96–111 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  31. Mansour, Y., Schieber, B.: The Intractability of bounded Protocols for On-Line Sequence Transmission over Non-FIFO Channels. Journal of the ACM 39(4), 783–799 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  32. Postel, J.: Internet Protocol. Internet Engineering Task Force Request For Comments 791 (1981)

    Google Scholar 

  33. Reed, B.: Finding Approximate Separators and Computing Treewidth Quickly. In: 24th ACM Symposium on Theory of Computing (STOC), pp. 221–228 (1992)

    Google Scholar 

  34. Robertson, N., Seymour, P.D.: Graph Minors. III. Planar Tree-Width. Journal of Combin. Theory B 36, 49–64 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  35. Robertson, N., Seymour, P.D.: Graph Minors. V. Excluding a planar graph. Journal of Combin. Theory B 41, 92–114 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  36. Robertson, N., Seymour, P.D., Thomas, R.: Quickly excluding a planar graph. Journal of Combin. Theory B 62, 323–348 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  37. Stenning, N.: A Data Transfer Protocol. Computer Networks 1(2), 99–110 (1976)

    Google Scholar 

  38. Tempero, E., Ladner, R.: Recoverable Sequence Transmission Protocols. Journal of the ACM 42(5), 1059–1090 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  39. Vishkin, U.: A Distributed Orientation Algorithm. IEEE Transaction on Information Theory 29, 624–629 (1983)

    Article  Google Scholar 

  40. Wang, D.-W., Zuck, L.: Tight Bounds for the Sequence Transmission Problem. In: 8th ACM Symposium on Principles of Distributed Computing (PODC), pp. 73–83 (1989)

    Google Scholar 

  41. Wang, D.-W., Zuck, L.: Real-Time Sequence Transmission Problem. In: 10th ACM Symposium on Principles of Distributed Computing (PODC), pp. 111–124 (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. CNRS, Laboratoire de Recherche en Informatique, Univ. Paris-Sud, France

    Pierre Fraigniaud

  2. Laboratoire Bordelais de Recherche en Informatique, Univ. Bordeaux I, France

    Cyril Gavoille

Authors
  1. Pierre Fraigniaud
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  2. Cyril Gavoille
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Editor information

Editors and Affiliations

  1. University of Toronto,  

    Faith Ellen Fich

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© 2003 Springer-Verlag Berlin Heidelberg

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Fraigniaud, P., Gavoille, C. (2003). Lower Bounds for Oblivious Single-Packet End-to-End Communication. In: Fich, F.E. (eds) Distributed Computing. DISC 2003. Lecture Notes in Computer Science, vol 2848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39989-6_15

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  • DOI: https://doi.org/10.1007/978-3-540-39989-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20184-7

  • Online ISBN: 978-3-540-39989-6

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