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
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Aloupis, Greg; Cardinal, Jean; Collette, Sébastien; Hurtado, Ferran; Langerman, Stefan; O'Rourke, Joseph; and Palop, Belén, "Highway Hull Revisited" (2010). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/38
Comments
Peer reviewed accepted manuscript. Licensed CC-BY-NC-ND at the publisher's request.