Shiri Chechik
ABSTRACT
We consider the problem of compact routing in weighted general undirected graphs, in which the goal is to construct local routing tables that allow information to be sent on short paths in the network. In this paper the first improvement to the work of Thorup and Zwick [SPAA'01] is presented. Specifically, we construct an improved routing scheme obtaining for every k routing tables of size Õ(n1/k log D), and stretch (4 -- α)k -- β for some absolute constants α, β > 0, where D is the normalized diameter. This provides a positive answer to a main open question in this area as to the existence of a routing scheme with stretch c • k for some constant c < 4.
- I. Abraham, C. Gavoille, and D. Malkhi. Routing with improved communication-space trade-off. In Proc. 18th Annual Conference on Distributed Computing (DISC), 305--319, 2004.Google Scholar
Cross Ref
- I. Abraham, C. Gavoille, D. Malkhi, N. Nisan, and M. Thorup. Compact name-independent routing with minimum stretch. In Proc. 16th Annual ACM Symposium on Parallel Algorithms and Architecture (SPAA), 20--24, 2004. Google ScholarDigital Library
- M. Arias, L. Cowen, K. Laing, R. Rajaraman, and O. Taka, Compact routing with name independence. In Proc. 15th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), 184--192, 2003. Google ScholarDigital Library
- B. Awerbuch, A. Bar-Noy, N. Linial, and D. Peleg. Compact distributed data structures for adaptive routing. In Proc. 21st ACM Symp. on Theory of Computing (STOC), 479--489, 1989. Google ScholarDigital Library
- B. Awerbuch, A. Bar-Noy, N. Linial, and D. Peleg. Improved routing strategies with succinct tables. In J. Algorithms, 11(3):307--341, 1990. Google ScholarDigital Library
- B. Awerbuch and D. Peleg. Sparse partitions. In Proc. 31st IEEE Symp. on Foundations of Computer Science (FOCS), 503--513, 1990. Google ScholarDigital Library
- L. J. Cowen. Compact routing with minimum stretch. J. Alg., 38:170--183, 2001. Google ScholarDigital Library
- T. Eilam, C. Gavoille, and D. Peleg. Compact routing schemes with low stretch factor. In J. Algorithms, 46:97--114, 2003. Google ScholarDigital Library
- P. Erdős. Extremal problems in graph theory. In Theory of graphs and its applications, pages 29--36, 1964.Google Scholar
- P. Fraigniaud and C. Gavoille. Memory requirement for universal routing schemes. In Proc. 14th ACM Symp. on Principles of Distributed Computing (PODC), 223--230, 1995. Google ScholarDigital Library
- P. Fraigniaud and C. Gavoille. Routing in Trees. In 28th Int'l Coll. on Automata, Languages and Programming (ICALP), 757--772, 2001. Google ScholarDigital Library
- C. Gavoille and M. Gengler. Space-efficiency for routing schemes of stretch factor three. In J. Parallel Distrib. Comput., 61:679--687, 2001. Google ScholarDigital Library
- C. Gavoille and D. Peleg. Compact and localized distributed data structures. In Distributed Computing, 16:111--120, 2003. Google ScholarDigital Library
- C. Gavoille and C. Sommer. Sparse spanners vs. compact routing. In Proc. 23th ACM Symp. on Parallel Algorithms and Architectures (SPAA), 225--234, 2011. Google ScholarDigital Library
- D. Peleg. Distributed computing: a locality-sensitive approach. In SIAM, 2000. Google ScholarDigital Library
- D. Peleg and E. Upfal. A trade-off between space and efficiency for routing tables. In J. ACM, 36(3):510--530, 1989. Google ScholarDigital Library
- M. Thorup and U. Zwick. Compact routing schemes. In Proc. 13th ACM Symp. on Parallel Algorithms and Architectures (SPAA), 1--10, 2001. Google ScholarDigital Library
- M. Thorup and U. Zwick. Approximate distance oracles. In J. ACM, 52, 1--24, 2005. Google ScholarDigital Library
Index Terms
- Compact routing schemes with improved stretch
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