Farthest Voronoi Diagrams under Travel Time Metrics

Abstract

AbstractGiven a set of roads in the plane with assigned speed, a traveler is assumed to move at the specified speed along each road, and at unit speed out of the roads. We are interested in the minimum travel time when we travel from one point in the plane to another, which defines a travel time metric. We study the farthest Voronoi diagram under this travel time metric, providing first nontrivial bounds on its combinatorial and computational complexity. Our approach is based on structural observations and recently known algorithmic technique. In particular, we show that if we are given a set of m isothetic roads with equal speed, then the diagram of n sites on the L 1 plane has Θ(nm) complexity and can be computed in O(nmlog3(n + m)) time in the worst case.KeywordsShort PathVoronoi DiagramTransportation NetworkMedial EdgeMinimum Travel TimeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.