Oracles for Distances Avoiding a Failed Node or Link
نویسندگان
چکیده
منابع مشابه
Oracles for Distances Avoiding a Failed Node or Link
We consider the problem of preprocessing an edge-weighted directed graph G to answer queries that ask for the length of a shortest path from any given vertex x to another given vertex y avoiding an arbitrary vertex or edge. As a natural application, this problem models routing in networks subject to node or link failures. We describe a deterministic oracle with constant query time for this prob...
متن کاملOracles for Distances Avoiding a Node or Link Failure∗
We consider the problem of preprocessing an edge-weighted directed graph G to answer queries that ask for the shortest distance from any given node x to any other node y avoiding an arbitrary failed node or link. We describe an oracle (i.e, a simple data structure) for such queries that can be stored in O(n log n) space, and which allows queries to be answered in O(1) time, where n is the numbe...
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Let G = (V,E) be a directed planar graph on n = |V | vertices, and let s ∈ V be any fixed source vertex. We show that G can be preprocessed in O(n polylogn) time to build a data structure of O(n polylogn) size which can answer the following query in O(log n) time for any u, v ∈ V : report distance from s to v in the graph G\{u} We also address the all-pairs version of this problem and present a...
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Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. Unless stated otherwise, we assume all graphs to be planar and undirected. In FOCS 2001 (J. ACM 2004), Thorup introduce...
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We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separators for planar graphs, discovered by Lipton and Tarjan [2], in order to divide the graph into smaller subgraphs. For a planar graph with n nodes, the algorithmic variant considered uses O(n(log n)/ ) preprocessing ti...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2008
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539705429847