Shortest Rectilinear Path Queries to Rectangles in a Rectangular Domain

Abstract

Given a set of open axis-aligned disjoint rectangles in the plane, each of which behaves as both an obstacle and a target, we seek to find shortest obstacle-avoiding rectilinear paths from a query to the nearest target and the farthest target. In our problem, the distance to a target is determined by the point on the target achieving the minimum or maximum geodesic distance among all points on the boundary of the target. This problem arises in facility location and robot motion planning problems. We show how to construct a data structure for such shortest path queries to the nearest and farthest neighbors efficiently.