@inproceedings{34fe3a68c8a541b19e47474fc143d41c,
title = "Preprocess, Set, query!",
abstract = "Thorup and Zwick [J. ACM and STOC'01] in their seminal work introduced the notion of distance oracles. Given an n-vertex weighted undirected graph with m edges, they show that for any integer k ≥ 1 it is possible to preprocess the graph in {\~O} (mm1/k) time and generate a compact data structure of size O(kn 1+1/k). For each pair of vertices, it is then possible to retrieve an estimated distance with multiplicative stretch 2k-1 in O(k) time. For k=2 this gives an oracle of O(n 1.5) size that produces in constant time estimated distances with stretch 3. Recently, Pǎtra{\c s}cu and Roditty [FOCS'10] broke the long-standing theoretical status-quo in the field of distance oracles and obtained a distance oracle for sparse unweighted graphs of O(n 5/3) size that produces in constant time estimated distances with stretch 2. In this paper we show that it is possible to break the stretch 2 barrier at the price of non-constant query time. We present a data structure that produces estimated distances with 1+ε stretch. The size of the data structure is O(nm 1-ε′) and the query time is {\~O}(m1-ε′). Using it for sparse unweighted graphs we can get a data structure of size O(n 1.86) that can supply in O(n 0.86) time estimated distances with multiplicative stretch 1.75.",
author = "Ely Porat and Liam Roditty",
year = "2011",
doi = "10.1007/978-3-642-23719-5_51",
language = "الإنجليزيّة",
isbn = "9783642237188",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "603--614",
booktitle = "Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings",
note = "19th Annual European Symposium on Algorithms, ESA 2011 ; Conference date: 05-09-2011 Through 09-09-2011",
}