Approximate distance oracles for graphs with dense clusters

Authors:
Mattias Andersson;Joachim Gudmundsson;Christos Levcopoulos
Affiliations:
Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden;National ICT Australia Ltd, Sydney, Australia;Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden
Venue:
Computational Geometry: Theory and Applications
Year:
2007

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Abstract

Let H"1=(V,E"1) be a collection of N pairwise vertex disjoint O(1)-spanners where the weight of an edge is equal to the Euclidean distance between its endpoints. Let H"2=(V,E"2) be the graph on V with M edges of non-negative weight. The union of the two graphs is denoted G=(V,E"1@?E"2). We present a data structure of size O(M^2+nlogn) that answers (1+@e)-approximate shortest path queries in G in constant time, where @e0 is constant.