The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation...

In this paper, we introduce and study the Non-Uniform k-Center (NUkC) problem. Given a finite metric space (X, d) and a collection of balls of radii {r1 ≥ · · · ≥ rk}, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation α, such that the union of balls of radius α · ri around the ith center covers all the points in X . This problem naturally...

In a graph G, the p-center problem is to identify p vertices of G for locating some kind of facilities such that the maximum among the distances from all vertices to their nearest facility is minimized. In this paper, we propose an O(n)-time algorithm for computing a 2-center in a chordal graph with maximum degree at most three, where a graph is chordal if every induced cycle of length at least...

Let G(V, E, W) be a graph with n-vertex-set V and m-edge-set E in which each edge e is associated with a positive distance W(e). The p-Center problem is to locate some kind of facilities at p vertices of G to minimize the maximum distance between any vertex and the nearest facility corresponding to that vertex. This paper proposes an additional practical constraint. We restrict that the p verti...

The obnoxious center problem in a graph G asks for a location on an edge of the graph such that the minimum weighted distance from this point to a vertex of the graph is as large as possible. We derive algorithms with linear running time for the cases when G is a path or a star, thus improving previous results of Tamir. For subdivided stars we present an algorithm of running time O(n log n). Fo...

The k center problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality so that the maximum distance of any node to its nearest center is minimized In this paper we consider a generalization of this problem where given a number p we wish to place k centers so as to minimize the maximum distance of any ...

In this paper we initiate the study of the heterogeneous capacitated k-center problem: given a metric space X = (F ∪C, d), and a collection of capacities. The goal is to open each capacity at a unique facility location in F , and also to assign clients to facilities so that the number of clients assigned to any facility is at most the capacity installed; the objective is then to minimize the ma...

This paper addresses a rollon–rolloff waste collection vehicle routing problem which involves large containers that collect huge amounts of waste from construction sites and shopping malls. In this problem, vehicles could only move one container at a time between customers’ locations, a depot, a disposal center, and a recycling center site. Other than a disposal center, a recycling ...

Let G(V, E, W) be a graph n vertices and m edges, where each edge e is associated with a positive distance W(e). The traditional p-Center problem is to locate some kind of facilities at p vertices of G to minimize the maximum distance between any vertex and its nearest facility. This paper proposes a practical constraint: the subgraph induced by the p facility vertices must be connected and the...

We study a traveling salesman problem where the path is optimized with a cost function that includes its length L as well as a certain measure C of its distance from the geometrical center of the graph. Using simulated annealing (SA) we show that such a problem has a transition point that separates two phases differing in the scaling behavior of L and C, in efficiency of SA, and in the shape of...