Given n demand points in the plane, the p-center problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo& point to its respective nearest supply point. The p-median problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the p-center and the p-media problems relative to both the...

the thermodynamic properties of fluids can be predicted using the global equations of state. among these thermodynamic properties of fluids, we choose the densities of the liquid and vapor phases. this paper considers the application of the crossover model to the vapor-liquid rectilinear diameter of sulfurhexafluoride. we also present a comparison of the crossover model equation with the experi...

This paper considers the problem of finding the least cost rectilinear distance path in the presence of convex polygonal congested regions. An upper bound for the number of entry/exit points for a congested region is obtained. Based on this key finding, we demonstrate that there are a finite, though exponential number of potential least cost paths between a specified pair of origin-destination ...

It is proved that any rectilinear polygon on n vertices, possibly with holes, can be partitioned into at most n 4 rectilinear stars each of size at most 12.

A pseudolinear (respectively, rectilinear) drawing of a graph G is optimal if it has the smallest number of crossings among all pseudolinear (respectively, rectilinear) drawings of G. We show that the convex hull of every optimal pseudolinear drawing of the complete graph Kn is a triangle. This is closely related to the recently announced result that the convex hull of every optimal rectilinear...

Area and axial flow variations on rectilinear vortex tubes are considered. The state of the flow is characterized by two dependent variables, a core area, and an azimuthal circulation per unit length, which vary in time and in distance along the length of the tube. Nonlinear integrodifferential equations of motion for these variables are derived by taking certain integrals of the vorticity tran...

For a set S of n points in the plane, a Manhattan network on S is a geometric network G(S) such that, for each pair of points in S, G(S) contains a rectilinear path between them of length equal to their distance in the L1-metric. The minimum Manhattan network problem is a problem of finding a Manhattan network of minimum length. Gudmundsson, Levcopoulos, and Narasimhan proposed a 4-approximatio...

In this paper a single facility location problem with multiple relocation opportunities is investigated. The weight associated with each demand point is a known function of time. We consider either rectilinear, or squared Euclidean, or Euclidean distances. Relocations can take place at pre-determined times. The objective function is to minimize the total location and relocation costs. An algori...

We present e cient algorithms for two problems of facility location. In both problems we want to optimize the location of two facilities with respect to n given sites. The rst problem, the continuous version, has no restrictions for facility locations but in the second one, the discrete version, facilities are chosen from a speci ed set of possible locations. We consider the rectilinear metric ...