Abstract
This article focuses on routing messages along shortest paths in tree networks, using compact distributed data structures. We mainly prove that n-node trees support routing schemes with message headers, node addresses, and local memory space of size O(log n) bits, and such that every local routing decision is taken in constant time. This improves the best known routing scheme by a factor of O(log n) in term of both memory requirements and routing time. Our routing scheme requires headers and addresses of size slightly larger than log n, motivated by an inherent trade-off between address-size and memory space, i.e., any routing scheme with addresses on log n bits requires Ω(√n) bits of local memory-space. This shows that a little variation of the address size, e.g., by an additive O(log n) bits factor, has a significant impact on the local memory space.
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References
B. Awerbuch AND D. Peleg, Sparse partitions, in 31th Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society Press, 1990, pp. 503–513.
L. J. Cowen, Compact routing with minimum stretch, in 10th Symposium on Discrete Algorithms (SODA), ACM-SIAM, 1999, pp. 255–260.
T. Eilam, C. Gavoille, AND D. Peleg, Compact routing schemes with low stretch factor, in 17th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM PRESS, Aug. 1998, pp. 11–20.
C. Gavoille, A survey on interval routing, Theoretical Computer Science, 245 (2000), pp. 217–253.
C. Gavoille AND S. Pérennès, Memory requirement for routing in distributed networks, in 15th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM PRESS, May 1996, pp. 125–133.
M. J. Hall, Combinatorial Theory (second edition), Wiley-Interscience Publication, 1986.
J. I. Munro, Tables, in 16th FST&TCS, vol. 1180 of Lectures Notes in Computer Science, Springer-Verlag, 1996, pp. 37–42.
J. I. Munro AND V. Raman, Succinct representation of balanced parentheses, static trees and planar graphs, in 38th Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society Press, Oct. 1997, pp. 118–126.
D. Peleg, Proximity-preserving labeling schemes and their applications, in 25th International Workshop, Graph-Theoretic Concepts in Computer Science (WG), vol. 1665 of Lecture Notes in Computer Science, Springer, June 1999, pp. 30–41.
D. Peleg AND E. Upfal, A trade-off between space and efficiency for routing tables, Journal of the ACM, 36 (1989), pp. 510–530.
N. Santoro AND R. Khatib, Labelling and implicit routing in networks, The Computer Journal, 28 (1985), pp. 5–8.
M. Thorup AND U. Zwick, Compact routing schemes, in 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), ACM PRESS, July 2001. To appear.
J. VAN Leeuwen AND R. B. Ttan, Interval routing, The Computer Journal, 30 (1987), pp. 298–307.
R. Warlimont, Factorisatio numerorum with constraints, Journal of Number Theory, 45 (1993), pp. 186–199.
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Fraigniaud, P., Gavoille, C. (2001). Routing in Trees. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_62
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DOI: https://doi.org/10.1007/3-540-48224-5_62
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