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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
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)
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)
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)
Afek, Y., Gafni, E.: Bootstrap Network Resynchonization. In: 10th ACM Symposium on Principles of Distributed Computing (PODC), pp. 295–307 (1991)
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)
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)
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)
Amir, E.: Efficient approximation for triangulation of minimum treewidth. In: 17th Conference on Uncertainty in Artificial Intelligence, UAI (2001)
Arnborg, S.: Efficient Algorithms for Combinatorial Problems on Graphs with Bounded Decomposability-A Survey. BIT 25, 2–23 (1985)
Arnborg, S., Corneil, D., Proskurowski, A.: Complexity of Finding Embeddings in a fc-Tree. SIAM J. Alg. Disc. Meth. 8, 277–284 (1987)
Awerbuch, B., Even, S.: Reliable Broadcast Protocols in Unreliable Networks. Networks 16, 381–396 (1986)
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)
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)
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)
Bodlaender, H.: A Tourist Guide through Treewidth. Acta Cybernetica 11, 1–21 (1993)
Bodlaender, H.: A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)
Bodlaender, H., Gilbert, J., Hafsteinsson, H., Kloks, T.: Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree. Journal of Algorithms 18, 238–255 (1995)
Bouchitté, V., Kratsch, D., Müller, H., Todinca, I.: On treewidth approximations. In: 1st Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW (2001)
Diestel, R.: Graph Theory, 2nd edn. Springer, New York (2000)
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)
Dolev, S., Welch, J.: Crash Resilient Communication in Dynamic Networks. IEEE Transactions on Computers 46(1), 14–26 (1997)
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)
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)
Fich, F.: End-to-End Communication Protocols. In: 2nd Int. Conference on Principles of Distributed Systems (OPODIS), Hermes, pp. 37–43 (1998)
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)
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)
Herzberg, A.: Connection-Based Communication in Dynamic Networks. In: 11th ACM Symposium on Principles of Distributed Computing (PODC), pp. 13–24 (1992)
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)
Ladner, R., LaMarca, A., Tempero, E.: Counting Protocol for Reliable End-to-End Transmission. Journal of Computer and System Sciences 56, 96–111 (1998)
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)
Postel, J.: Internet Protocol. Internet Engineering Task Force Request For Comments 791 (1981)
Reed, B.: Finding Approximate Separators and Computing Treewidth Quickly. In: 24th ACM Symposium on Theory of Computing (STOC), pp. 221–228 (1992)
Robertson, N., Seymour, P.D.: Graph Minors. III. Planar Tree-Width. Journal of Combin. Theory B 36, 49–64 (1984)
Robertson, N., Seymour, P.D.: Graph Minors. V. Excluding a planar graph. Journal of Combin. Theory B 41, 92–114 (1986)
Robertson, N., Seymour, P.D., Thomas, R.: Quickly excluding a planar graph. Journal of Combin. Theory B 62, 323–348 (1994)
Stenning, N.: A Data Transfer Protocol. Computer Networks 1(2), 99–110 (1976)
Tempero, E., Ladner, R.: Recoverable Sequence Transmission Protocols. Journal of the ACM 42(5), 1059–1090 (1995)
Vishkin, U.: A Distributed Orientation Algorithm. IEEE Transaction on Information Theory 29, 624–629 (1983)
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)
Wang, D.-W., Zuck, L.: Real-Time Sequence Transmission Problem. In: 10th ACM Symposium on Principles of Distributed Computing (PODC), pp. 111–124 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Springer Book Archive