Document Type

Article

Publication Date

2-2010

Publication Title

Computational Geometry

Abstract

A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in H(S,H), using the highway time distance. We provide a Θ(nlogn) worst-case time algorithm to find the highway hull under the L1 metric, as well as an O(nlog2n) time algorithm for the L2 metric which improves the best known result of O(n2) [F. Hurtado, B. Palop, V. Sacristán, Diagramas de Voronoi con distancias temporales, in: Actas de los VIII Encuentros de Geometra Computacional, 1999, pp. 279–288 (in Spanish); B. Palop, Algorithmic problems on proximity and location under metric constraints, PhD thesis, Universitat Politècnica de Catalunya, 2003]. We also define and construct the useful region of the plane: the region that a highway must intersect in order that the shortest path between at least one pair of points uses the highway.

Keywords

Time distance, Convex hull, Transportation facility

Volume

43

Issue

2

First Page

115

Last Page

130

DOI

dx.doi.org/10.1016/j.comgeo.2009.06.001

ISSN

0925-7721

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Comments

Peer reviewed post-print. Licensed CC-BY-NC-ND at the publisher's request.

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