Let G = (V,E) be an unweighted undirected graph with n-vertices and m-edges, and let k > 2 be an integer. We present a routing scheme with a poly-logarithmic header size, that given a source s and a destination t at distance Δ from s, routes a message from s to t on a path whose length is O(kΔ + m1/k). The total space used by our routing scheme is Õ (mnO(1/), which is almost linear in the number of edges of the graph. We present also a routing scheme with Õ(nO(1/) header size, and the same stretch (up to constant factors). In this routing scheme, the routing table of every v ∈ V is at most Õ(knO(1/)deg(v)), where deg(v) is the degree of v in G. Our results are obtained by combining a general technique of Bernstein [6], that was presented in the context of dynamic graph algorithms, with several new ideas and observations.
CITATION STYLE
Roditty, L., & Tov, R. (2014). Close to linear space routing schemes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8784, pp. 182–196). Springer Verlag. https://doi.org/10.1007/978-3-662-45174-8_13
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