We present a data structure that allows to preprocess a rectilinear polygon with n vertices such that, for any two query points, the shortest path in the rectilinear link or L 1-metric can be reported in time O(log n + k) where k is the link length of the shortest path. If only the distance is of interest, the query time reduces to O(log n). Furthermore, if the query points are two vertices, th...

In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set P of n (weighted) uncertain points in the plane and each uncertain point has m possible locations each associated with a probability for the point appearing at that location. The goal is to find a point q∗ in the plane which minimizes the maximum expected rectiline...

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter...

In this paper, a single-source capacitated multifacility location problem with rectilinear distance under unbalanced transportation constraints is studied. The problem is formulated as a mixed integer linear programming problem of which the objective function is the sum of nonlinear functions. An algorithm under decomposition approach combining with logic based techniques is developed. Using th...

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...

In this paper, we consider the weighted rectilinear min-sum facility problem to minimize the sum of the weighted rectilinear distance between the given points and a new added point. The core problem is the problem in its one dimensional cases noted as the weighted median problem. We present efficient algorithms for optimally solving the weighted median problem. The computational experiments dem...

The rectilinear Steiner tree problem requires a shortest tree spanning a given vertex subset in the plane with rectilinear distance. It was proved that the output length of Zelikovsky's 25] and Berman/Ramaiyer 3] heuristics is at most 1.375 and 97 72 1:347 of the optimal length, respectively. It was claimed that these bounds are not tight. Here we improve these bounds to 1.3125 and 61 48 1:271,...

Computing rectilinear shortest paths in two dimensions has been solved optimally using a number of different techniques. A variety of related problems have been solved, including minimizing the number of bends in the path, the total rectilinear distance, or some combination of both. However, solutions to the 3D versions of these problems are less common. We propose a solution to the 3D minimum-...