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...

An optimal line is sought in the Euclidean plane in terms of the ordered median criterion, when the set of existing facilities are points with arbitrary positive associated weights. By way of geometric duality a dominating set for such a line is found. This allows the construction of an algorithm to solve the problem in O(n4).

Given an edge-weighted graph G = (V, E), the Hamiltonian p-median problem (HpMP) asks for determining p cycles in G whose total length is minimized such that each node is contained in exactly one cycle. As the travelling salesman problem (TSP) corresponds to the choice p = 1, the HpMP can be interpreted as a generalization of the TSP. In this paper, we study the polytope associated with the HpM...

We present a fast approximation algorithm for the 1-median problem. Our algorithm can be applied to metric undirected graphs with node weight. Given a node v, our algorithm repeatedly executes a process of finding a node with higher centrality,in which an approximate centrality of each node v’ is calculated for the subgraph called the best kNSPGS of (v,v’). The best kNSPGS of (v,v’) is a subgra...

In this paper we propose several heuristics for the Uncapacitated -Allocation -Hub Median Problem. In the classical -hub problem, given a set of nodes with pairwise traffic demands, we must select of them as hub locations and route all traffics through them at a minimum cost. We target here an extension, called the -allocation -hub median problem, recently proposed by Yaman (2011), in which eve...

Capacitated p-median problem (CPMP) is an important variation of facility location problem in which p capacitated medians are economically selected to serve a set of demand vertices so that the total assigned demand to each of the candidate medians must not exceed its capacity. The classical CPMP uses a network in a Euclidean plane such that distance between any two points in the network is the...

In this paper, we revisit the classical k-median problem: Given n points in a metric space, select k centers so as to minimize the sum of distances of points to their closest center. Using the standard LP relaxation for k-median, we give an efficient algorithm to construct a probability distribution on sets of k centers that matches the marginals specified by the optimal LP solution. Our algori...

In this paper we present a hybrid approach to integrative clustering based on the p-median problem with clients’ preferences. We formulate the problem of simultaneous clustering of a set of objects, characterized by two sets of features, as a bi-level p-median model. An exact approach involving a branchand-cut method combined with the simulated annealing algorithm is used, that allows one to fi...

We present two heuristic methods for solving the Discrete Ordered Median Problem (DOMP), for which no such approaches have been developed so far. The DOMP generalizes classical discrete facility location problems, such as the p-median, p-center and Uncapacitated Facility Location problems. The first procedure proposed in this paper is based on a genetic algorithm developed by Moreno Vega [MV96]...

This paper presents an exact algorithm, a constructive heuristic algorithm, and a metaheuristic for the Hamiltonian p-Median Problem (HpMP). The exact algorithm is a branch-and-cut algorithm based on an enhanced p -median based formulation, which is proved to dominate an existing p -median based formulation. The constructive heuristic is a giant tour heuristic, based on a dynamic programming fo...