Abstract
The design of compact routing schemes in trees form the kernel of sophisticated strategies for compact routing in arbitrary graphs. This paper focuses on the space complexity for routing messages along shortest paths in trees. It was recently shown that the family of n-node trees supports routing schemes using addresses and routing tables of size O(log2 n/log log n) bits per node, if the output port numbers of each node are chosen by an adversary. This paper shows that this result is tight, that is the sum of the sizes of the address and of the local routing table is at least Ω(log2 n/ log log n) bits for some node of some tree.
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References
Baruch Awerbuch and David Peleg. Sparse partitions. In 31th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 503–513. IEEE Computer Society Press, October 1990.
Baruch Awerbuch and David Peleg. Routing with polynomial communicationspace trade-off. SIAM Journal on Discrete Mathematics, 5(2):151–162, May 1992.
Lenore J. Cowen. Compact routing with minimum stretch. Journal of Algorithms, 38:170–183, 2001.
Tamar Eilam, Cyril Gavoille, and David Peleg. Compact routing schemes with low stretch factor. In 17th Annual ACM Symposium on Principles of Distributed Computing (PODC), pages 11–20. ACM PRESS, August 1998.
Paul Erdös. Extremal problems in graph theory. In Publ. House Cszechoslovak Acad. Sci., Prague, pages 29–36, 1964.
Pierre Fraigniaud and Cyril Gavoille. Routing in trees. In 28th International Colloquium on Automata, Languages and Programming (ICALP), volume 2076 of Lecture Notes in Computer Science, pages 757–772. Springer, July 2001.
Cyril Gavoille. A survey on interval routing. Theoretical Computer Science, 245(2):217–253, 2000.
Cyril Gavoille. Routing in distributed networks: Overview and open problems. ACM SIGACT News — Distributed Computing Column, 32(1):36–52, March 2001.
Cyril Gavoille and David Peleg. Compact and localized distributed data structures. Research Report RR-1261-01, LaBRI, University of Bordeaux, 351, cours de la Libération, 33405 Talence Cedex, France, August 2001. To appear in Journal of Distributed Computing.
Cyril Gavoille, David Peleg, Stéphane Pérennes, and Ran Raz. Distance labeling in graphs. In 12th Symposium on Discrete Algorithms (SODA), pages 210–219. ACM-SIAM, January 2001.
David Peleg. Informative labeling schemes for graphs. In 25th International Symposium on Mathematical Foundations of Computer Science (MFCS), volume 1893 of Lecture Notes in Computer Science, pages 579–588. Springer, August 2000.
David Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167–176, 2000.
David Peleg and Eli Upfal. A trade-off between space and efficiency for routing tables. Journal of the ACM, 36(3):510–530, July 1989.
Mikkel Thorup and Uri Zwick. Approximate distance oracles. In 33rd Annual ACM Symposium on Theory of Computing (STOC), pages 183–192, Hersonissos, Crete, Greece, July 2001.
Mikkel Thorup and Uri Zwick. Compact routing schemes. In 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pages 1–10, Hersonissos, Crete, Greece, July 2001. ACM PRESS.
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Fraigniaud, P., Gavoille, C. (2002). A Space Lower Bound for Routing in Trees. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_4
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DOI: https://doi.org/10.1007/3-540-45841-7_4
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