Rectilinear paths among rectilinear obstacles

Rectilinear Paths among Rectilinear Obstacles

Given a set of obstacles and two distinguished points in the plane the problem of nding a collision free path subject to a certain optimization function is a fundamental problem that arises in many elds, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinea...

Bicriteria Rectilinear Shortest Paths among Rectilinear Obstacles in the Plane

Given a rectilinear domain P of h pairwise-disjoint rectilinear obstacles with a total of n vertices in the plane, we study the problem of computing bicriteria rectilinear shortest paths between two points s and t in P. Three types of bicriteria rectilinear paths are considered: minimum-link shortest paths, shortest minimum-link paths, and minimum-cost paths where the cost of a path is a non-de...

Rectilinear Path Problems among Rectilinear Obstacles Revisited

We present eecient algorithms for nding rectilinear collision-free paths between two given points among a set of rectilinear obstacles. Our results improve the time complexity of previous results for nding the shortest rectilinear path, the minimum-bend shortest rectilinear path, the shortest minimum-bend rectilinear path and the minimum-cost rectilinear path. For nding the shortest rectilinear...

k-Link Rectilinear Shortest Paths Among Rectilinear Obstacles in the Plane

We present an algorithm for computing k-link rectilinear shortest paths among rectilinear obstacles in the plane. We extend the “continuous Dijkstra” paradigm to store the link distance information associated with each propagating “wavefront”. Our algorithm runs in time O(kn log n) and space O(kn), where n is the number of vertices of the obstacles. Previous algorithms for the problem had worst...

Rectilinear short path queries among rectangular obstacles