Javier Marenco

On the b-Coloring of Cographs and P 4 -Sparse Graphs

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every

A method for optimizing waste collection using mathematical programming: a Buenos Aires case study

t = \chi(G), \ldots, \chi_b(G)

A Framework for Scheduling Professional Sports Leagues

. We define a graph G to be b-monotonic if χb(H1) ≥ χb(H2) for every induced subgraph H1 of G, and every induced subgraph H2 of H1. In this work, we prove that P4-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming algorithm to compute the b-chromatic number in polynomial time within these graph classes.

Minimum sum set coloring of trees and line graphs of trees

In this paper we present a study of the polytope associated to a classic linear integer programming formulation of the graph coloring problem. We determine some families of facets. This is the initial step for the development of a branch-and-cut algorithm to solve large instances of the graph coloring problem.

Exploring the complexity boundary between coloring and list-coloring

A method is proposed that uses operations research techniques to optimize the routes of waste collection vehicles servicing dumpster or skip-type containers. The waste collection problem is reduced to the classic travelling salesman problem, which is then solved using the Concorde solver program. A case study applying the method to the collection system in the southern zone of Buenos Aires is also presented. In addition to the typical minimum distance criterion, the optimization problem incorporates the objective of reducing vehicle wear and tear as measured by the physics concept of mechanical work. The solution approach, employing graph theory and mathematical programming tools, is fully described and the data correction process is also discussed. The application of the proposed method minimized the distance travelled by each collection vehicle in the areas studied, with actual reductions ranging from 10 to 40% of the existing routes. The shortened distances led in turn to substantial decreases in work done and therefore in vehicle wear and tear. Extrapolation of the results to the entire southern zone of Buenos Aires indicates potential savings for the civic authorities of more than US

Chromatic scheduling polytopes coming from the bandwidth allocation problem in point-to-multipoint radio access systems

200 000 per year in addition to the qualitative impacts of less traffic disruption, less vehicle driver fatigue and less pollution.

An integer programming approach to a real-world recyclable waste collection problem in Argentina

Ship routing problems are a particular kind of routing problems where the vehicles to be routed are vessels or ships, usually in maritime environments. In contrast to land routing, ship routing has unique features, including overnight trips, disjoint time windows, not necessarily prespecified routes, and a great uncertainty derived from weather conditions. In this work we present a special ship routing problem, which incorporates many features present in general ship routing settings. We discuss aspects related with data gathering and updating, which are particularly difficult in the context of ship routing. Additionally, we present a GRASP algorithm to solve this problem. We apply our solution approach to a salmon feed supplier based in southern Chile, and present computational results on real data.

General cut-generating procedures for the stable set polytope

This paper introduces a framework for a highly constrained sports scheduling problem which is modeled from the requirements of various professional sports leagues. We define a sports scheduling problem, introduce the necessary terminology and detail the constraints of the problem. A set of artificial and real‐world instances derived from the actual problems solved for the professional sports league owners are proposed. We publish the best solutions we have found, and invite the sports scheduling community to find solutions to the unsolved instances. We believe that the instances will help researchers to test the value of their solution methods. The instances are available online.