New algorithms for shortest paths avoiding convex polygonal obstacles

Abstract

Two algorithms are presented for computing shortest paths in the plane avoiding convex polygonal obstacles. For the first algorithm the obstacles are assumed to consist of f disjoint convex polygons, for the second algorithm the f polygons may intersect pairwise at most twice. For finding the shortest path between two arbitrary query points the first algorithm takes time O(nlogn + f^2logn) and space O(n), the second algorithm preprocesses the polygons in time O(nlogn + f^3) and space O(n + f^2). Thereafter one query takes time O(nlogn + f^2).