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Communication dans un congrès

Querying approximate shortest paths in anisotropic regions

Abstract : We present a data structure for answering approximate shortest path queries ina planar subdivision from a fixed source. Let ρ ≥ 1 be a real number.Distances in each face of this subdivision are measured by a possiblyasymmetric convex distance function whose unit disk is contained in aconcentric unit Euclidean disk, and contains a concentric Euclidean disk withradius 1/ρ. Different convex distance functions may be used for differentfaces, and obstacles are allowed. Let ε be any number strictly between 0and 1. Our data structure returns a (1+ε)approximation of the shortest path cost from the fixed source to a querydestination in O(logρn/ε) time. Afterwards, a(1+ε)-approximate shortest path can be reported in time linear in itscomplexity. The data structure uses O(ρ2 n4/ε2 log ρn/ε) space and can be built in O((ρ2 n4)/(ε2)(log ρn/ε)2) time. Our time and space bounds do not depend onany geometric parameter of the subdivision such as the minimum angle.
Type de document :
Communication dans un congrès
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Déposant : Migration Prodinra <>
Soumis le : mercredi 3 juin 2020 - 17:18:08
Dernière modification le : vendredi 12 juin 2020 - 10:43:26




Siu-Wing Cheng, Hyeon-Suk Na, Antoine Vigneron, Yajun Wang. Querying approximate shortest paths in anisotropic regions. Twenty-third Annual Symposium on Computational Geometry, Jun 2007, Gyeongju, South Korea. ⟨10.1145/1247069.1247082⟩. ⟨hal-02750642⟩



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