SHORTEST PATH QUERIES IN RECTILINEAR WORLDS

Shortest path queries in rectilinear worlds

Rectilinear Shortest Path and Rectilinear Minimum Spanning Tree with Neighborhoods

We consider a setting where we are given a graph G = (R, E), where R = {R1, . . . , Rn} is a set of polygonal regions in the plane. Placing a point pi inside each region Ri turns G into an edge-weighted graph Gp , p = {p1, . . . , pn}, where the cost of (Ri, Rj) ∈ E is the distance between pi and pj . The Shortest Path Problem with Neighborhoods asks, for given Rs and Rt, to find a placement p ...

Euclidean Shortest Path Problem with Rectilinear Obstacles1

This paper presents new heuristic algorithms using the guided A* search method : Guided Minimum Detour (GMD) algorithm and Line-by-Line Guided Minimum Detour (LGMD) algorithm for finding optimal rectilinear (L,) shortest paths in the presence of rectilinear obstacles. The GMD algorithm runs O(nhr(1ogN) + tN) in time and takes O(N) in space, where N is the number of extended line segments includ...

Rectilinear short path queries among rectangular obstacles

Computing a rectilinear shortest path amid splinegons in plane

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain S to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of this, we define a polygonal domain P from S and transform a rectilinear shortest path computed in P to a path between s and t amid splinegon obstacles in S. When ...