Shortest rectilinear path queries to rectangles in a rectangular domain

Abstract

Given a set of open axis-aligned disjoint rectangles, each of which plays 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. 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 data structures supporting such shortest path queries to the nearest and farthest neighbors efficiently.