2,328 research outputs found
Median problems in networks
The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.P-median, location modelling
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Consumer choice in competitive location models: Formulations and heuristics
A new direction of research in Competitive Location theory incorporates theories of Consumer Choice Behavior in its models. Following this direction, this paper studies the importance of consumer behavior with respect to distance or transportation costs in the optimality of locations obtained by traditional Competitive Location models. To do this, it considers different ways of defining a key parameter in the basic Maximum Capture model (MAXCAP). This parameter will reflect various ways of taking into account distance based on several Consumer Choice Behavior theories. The optimal locations and the deviation in demand captured when the optimal locations of the other models are used instead of the true ones, are computed for each model. A metaheuristic based on GRASP and Tabu search procedure is presented to solve all the models. Computational experience and an application to 55-node network are also presented.Distance, competitive location models, consumer choice behavior, GRASP, tabu
On the Properties of Gromov Matrices and their Applications in Network Inference
The spanning tree heuristic is a commonly adopted procedure in network
inference and estimation. It allows one to generalize an inference method
developed for trees, which is usually based on a statistically rigorous
approach, to a heuristic procedure for general graphs by (usually randomly)
choosing a spanning tree in the graph to apply the approach developed for
trees. However, there are an intractable number of spanning trees in a dense
graph. In this paper, we represent a weighted tree with a matrix, which we call
a Gromov matrix. We propose a method that constructs a family of Gromov
matrices using convex combinations, which can be used for inference and
estimation instead of a randomly selected spanning tree. This procedure
increases the size of the candidate set and hence enhances the performance of
the classical spanning tree heuristic. On the other hand, our new scheme is
based on simple algebraic constructions using matrices, and hence is still
computationally tractable. We discuss some applications on network inference
and estimation to demonstrate the usefulness of the proposed method
Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography
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
Graph médian généralisé via des minimisations alternées.
International audienceComputing a graph prototype may constitute a core element for clustering or classification tasks. However, its computation is an NP-Hard problem, even for simple classes of graphs. In this paper, we propose an efficient approach based on block coordinate descent to compute a generalized median graph from a set of graphs. This approach relies on a clear definition of the optimization process and handles labeling on both edges and nodes. This iterative process optimizes the edit operations to perform on a graph alternatively on nodes and edges. Several experiments on different datasets show the efficiency of our approach.Calculer un graphe prototype peut constituer une étape centrale pour des méthodes de clustering ou de classification. Toutefois, ce calcul est NP-difficile même pour des classes de graphes simples. Nous proposons dans ce papier une approche efficace basée sur une minimisation alternée pour calculer le graphe médian d'un ensemble. Cette approche s'appuie sur une définition claire du processus d'optimisation et inclue l'étiquetage à la fois des nœuds et des arêtes. Ce processus itératif optimise les opérations à effectuer alternativement sur les sommets et les arêtes. Plusieurs expériences sur des jeux de données différents montrent l'efficacité de notre approche
Fast and Robust Techniques for the Euclidean p-Median Problem with Uniform Weights
We discuss new solution techniques for the p-median problem, with the goal being to improve the solution time and quality of current techniques. In particular, we hybridize the discrete Lloyd algorithm and the vertex substitution heuristic. We also compare three starting point techniques and present a new solution method that provides consistently good results when appropriately initialized
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