This paper studies distance oracles and distance labeling scheme with local stretch. Informally we would like to provide stretch guarantees for the r closest nodes of each node. A distance oracle has local stretch k for r neighborhoods if for any u,v such that v = M(u,r′) and r′ ≤ r: dist(u, v) ≤ dĩst (u, v) ≤ kdist(u, v), where M(u,r′) is the r′ closest node to u and is the estimated distance returned by the distance oracle. For parameters r > 1, k > 1, we obtain labels of size O(r1/k ln1 - 1/k r + ln k), with local stretch of 2k - 1 for r neighborhoods in O(k) time, significantly improving the query time and stretch constant of [ABN09]. Moreover, our stretch guarantee of 2k - 1 matches the best known (and conjectured optimal) guarantees of standard distance oracles. © 2014 Springer-Verlag.
CITATION STYLE
Abraham, I., & Chechik, S. (2014). Distance labels with optimal local stretch. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8572 LNCS, pp. 52–63). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_5
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