Shortest Paths and Voronoi Diagrams with Transportation Networks Under General Distances
نویسندگان
چکیده
Transportation networks model facilities for fast movement on the plane. A transportation network, together with its underlying distance, induces a new distance. Previously, only the Euclidean and the L1 distances have been considered as such underlying distances. However, this paper first considers distances induced by general distances and transportation networks, and present a unifying approach to compute Voronoi diagrams under such a general setting. With this approach, we show that an algorithm for convex distances can be easily obtained.
منابع مشابه
Travel Time Distances Induced by Transportation Networks and General Underlying Distances
This paper considers a generalization of travel time distances by taking general underlying distance functions into account. We suggest a reasonable set of axioms defining a certain class of distance functions that can be facilitated with transportation networks. It turns out to be able to build an abstract framework for computing shortest path maps and Voronoi diagrams with respect to the indu...
متن کاملGeneralized Voronoi Diagrams on Polyhedral Terrains
We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...
متن کاملSOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS
Numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(FSPP). The main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...
متن کاملPursuit/Evasion Voronoi Diagrams∗
In typical 2D Voronoi diagrams, the distance from a site to a point in the plane is unaffected by the existance of other sites. In 2D pursuit/evasion Voronoi diagrams, the distance from an evader to a point is the length of the shortest path to that point that avoids all pursuers. Since pursuers can move, the paths that evaders follow to reach certain points in the plane can be quite complicate...
متن کاملGeneralized Source Shortest Paths on Polyhedral Surfaces
We present an algorithm for computing shortest paths and distances from a single generalized source (point, segment, polygonal chain or polygon) to any query point on a possibly non-convex polyhedral surface. The algorithm also handles the case in which polygonal chain or polygon obstacles on the polyhedral surface are allowed. Moreover, it easily extends to the case of several generalized sour...
متن کامل