We consider a constrained minimax single-facility location problem with addends on the plane with rectilinear distance. The problem is first formulated in a standard form, and then represented in terms of tropical mathematics as a constrained optimization problem. We apply methods and results of tropical optimization to obtain direct, explicit solutions to the optimization problem. The results ...

ÐThis paper discusses and experimentally compares distance-based acceleration algorithms for ray-tracing of volumetric data with an emphasis on the Chessboard Distance (CD) voxel traversal. The acceleration of this class of algorithms is achieved by skipping empty macro regions, which are defined for each background voxel of the volume. Background voxels are labeled in a preprocessing phase by ...

The diameter of a set S of points is the maximal distance between a pair of points in S. The center of S is the set of points that minimize the distance to their furthest neighbours. The problem of nding the diameter and center of a simple polygon with n vertices for diierent distance measures has been studied extensively in recent years. There are algorithms that run in linear time if the geod...

An instance of a p-median problem gives n demand points. The objective is to locate p supply points in order to minimize the total distance of the demand points to their nearest supply point. p-Median is polynomially solvable in one dimension but NP-hard in two or more dimensions, when either the Euclidean or the rectilinear distance measure is used. In this paper, we treat the p-median problem...

The unequal area facility layout problem has been studied using several distance metrics in the objective function, most commonly rectilinear distance and Euclidean distance between departmental centroids. This paper modifies the distance metric to consider material travel along the perimeter of the departments to and from input/output locations. This perimeter distance metric is used in the ob...

We consider the problem of weighted rectilinear approximation on the plane and offer both exact algorithms and heuristics with provable performance bounds. Let S = {(pi, wi)} be a set of n points pi in the plane, with associated distance-modifying weights wi > 0. We present algorithms for finding the best fit to S among x-monotone rectilinear polylines R with a given number k < n of horizontal ...