Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
Ken‐ichi Kawarabayashi, Philip N. Klein, Christian Sommer, Brown U · 2012
Abstract. A (1 + ɛ)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup) and, subsequently, minor-excluded graphs (Abraham and Gavoille). However, these require Ω(ɛ −1 n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minorexcluded graphs we give distance-oracle constructions that require only