Planar rectilinear shortest path computation using corridors

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...

Shortest path queries in rectilinear worlds

Constrained Shortest Path Computation

This paper proposes and solves a-autonomy and k-stops shortest path problems in large spatial databases. Given a source s and a destination d, an aautonomy query retrieves a sequence of data points connecting s and d, such that the distance between any two consecutive points in the path is not greater than a. A k-stops query retrieves a sequence that contains exactly k intermediate data points....

Acceleration of Shortest Path and Constrained Shortest Path Computation

We study acceleration methods for point-to-point shortest path and constrained shortest path computations in directed graphs, in particular in road and railroad networks. Our acceleration methods are allowed to use a preprocessing of the network data to create auxiliary information which is then used to speed-up shortest path queries. We focus on two methods based on Dijkstra’s algorithm for sh...