Publication IEICE TRANSACTIONS on Information and SystemsVol.E88-DNo.1pp.47-52 Publication Date: 2005/01/01 Online ISSN: DOI: 10.1093/ietisy/e88-d.1.47 Print ISSN: 0916-8532 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science) Category: Keyword: distributed algorithms, compact routing, stretch factor,

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Summary: Cowen gave a universal compact routing algorithm with a stretch factor of three and table-size of O(n^{2/3}log^{4/3}n) based on a simple and practical model. (The table-size is later improved to O(n^{1/2}log^{3/2}n).) This paper considers, using the same model, how the necessary table-size differs if the stretch factor must be less than three. It is shown that: (i) There is a routing algorithm with a stretch factor of two whose table-size is (n -+ 2)log n. (ii) There is a network for which any routing algorithm that follows the model and with a stretch factor of less than three needs a table-size of (n - 2)log n in at least one node. Thus, we can only reduce roughly an additive log n (i.e., table-entries) from the trivial table-size of n log n which obviously enables shortest-path routing. Furthermore it turns out that we can reduce only an additive log n (i.e., only one table-entry) from the trivial n log n if we have to achieve a stretch factor of less than two. Thus the algorithm (i) is (roughly) tight both in its stretch factor and in its table-size.