Shortest path queries among weighted obstacles in the rectilinear plane

Abstract

We study the problems of processing single-source and two-point shortest path queries among weighted polygonal obstacles in the rectilinear plane. For the single-source case, we construct a data structure in O(n log n) time and O(n logn) space, where n is the number of obstacle vertices; this data structure enables us to report the length of a shortest path between the source and any query point in O(logn) time, and an actual shortest path in O(logn+k) time, where k is the number of edges on the output path. For the two-point case, we construct a data structure in O(n2 log n) time and space; this data structure enables us to report the length of a shortest path between two arbitrary query points in O(log n) time, and an actual shortest path in O(log n+ k) time. Our work improves and generalizes the previously best-known results on computing rectilinear shortest paths among weighted polygonal obstacles. We also apply our techniques to processing twopoint L1 shortest obstacle-avoiding path queries among arbitrary (i.e., not necessarily rectilinear) polygonal obstacles in the plane. No algorithm for processing two-point shortest path queries among weighted obstacles was previously known.