Adaptive and compact discretization for weighted region optimal path finding

Abstract

This paper presents several results on the weighted region optimal path problem. An often-used approach to approximately solve this problem is to apply a discrete search algorithm to a graph Gε generated by a discretization of the problem; this graph guarantees to contain an ε-approximation of an optimal path between given source and destination points. We first provide a discretization scheme such that the size of Gε does not depend on the ratio between the maximum and minimum unit weights. This leads to the first ε-approximation algorithm whose complexity is not dependent on the unit weight ratio. We also introduce an empirical method, called adaptive discretization method, that improves the performance of the approximation algorithms by placing discretization points densely only in areas that may contain optimal paths. BUSHWHACK is a discrete search algorithm used for finding optimal paths in Gε. We added two heuristics to BUSHWHACK to improve its performance and scalability. © Springer-Verlag Berlin Heidelberg 2003.