We develop the heuristic PROBI for the probabilistic Euclidean k-median problem based on a coreset construction by Lammersen et al. [28]. Our algorithm computes a summary of the data and then uses an adapted version of k-means++ [5] to compute a good solution on the summary. The summary is maintained in a data stream, so PROBI can be used in a data stream setting on very large data sets. We exp...

Good heuristic solutions for large Multisource Weber problems can be obtained by solving related p-median problems in which potential locations of the facilities are users locations and then solving Weber problems for the sets of users of each facility. Weber's problem is to locate a facility in the Euclidean plane in order to minimize the sum of its (weighted) distances to the locations of a g...

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem.

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.

We present the first constant-factor approximation algorithm for the metric k-median problem. The k-median problem is one of the most well-studied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are relatively close with respect to some measure. For the metric k-median problem, we are given n poin...

The Reverse Greedy algorithm (RGREEDY) for the k-median problem works as follows. It starts by placing facilities on all nodes. At each step, it removes a facility to minimize the total distance to the remaining facilities. It stops when k facilities remain. We prove that, if the distance function is metric, then the approximation ratio of RGREEDY is between (logn/ log logn) and O(logn).  2005...

Résumé In this note, we present linear time algorithms for computing the median set of plane triangulations with inner vertices of degree ≥ 6 and plane quadrangulations with inner vertices of degree ≥ 4. Dans cette note, nous présentons un algorithme linéaire pour calculer l’ensemble médian de triangulations planaires dont les sommets intérieurs sont de degré ≥ 6 et de quadrangulations planaire...

The genomic median problem is an optimization problem inspired by a biological issue: it aims to find the chromosome organization of the common ancestor to multiple living species. It is formulated as the search for a genome that minimizes a rearrangement distance measure among given genomes. Several attempts have been reported for solving this NP-hard problem. These range from simple heuristic...

This paper deals with changing parameters of the 1-median problem in the plane with Manhattan metric within certain bounds such that the optimal objective value of the 1-median problem with respect to the new values of the parameters is maximized. An O(n log n) time algorithm is suggested that is mainly based on a fast search and prune procedure.

The convex ordered median problem is a generalization of the median, the k-centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP-hard even if the underlying network is a tree and the ordered median...