Computing L1 Shortest Paths Among Polygonal Obstacles in the Plane.

Given a point s and a set of h pairwise disjoint polygonal obstacles with a total of n vertices in the plane, suppose a triangulation of the space outside the obstacles is given; we present an O (n + h log h) time and O(n) space algorithm for building a data structure (called shortest path map) of size O(n) such that for any query point t, the length of an L 1 shortest obstacle-avoiding path from s to t can be computed in O (log n) time and the actual path can be reported in additional time proportional to the number of edges of the path. The previously best algorithm computes such a shortest path map in O (n log n) time and O(n) space. So our algorithm is faster when h is relatively small. Further, our techniques can be extended to obtain improved results for other related problems, e.g., computing the L 1 geodesic Voronoi diagram for a set of point sites among the obstacles. [ABSTRACT FROM AUTHOR]