A DSATUR-based algorithm for the Equitable Coloring Problem

This paper describes a new exact algorithm for the Equitable Coloring Problem, a coloring problem where the sizes of two arbitrary color classes differ in at most one unit. Based on the well known DSatur algorithm for the classic Coloring Problem, a pruning criterion arising from equity constraints is proposed and analyzed. The good performance of the algorithm is shown through computational experiments over random and benchmark instances.Fil: Méndez-Díaz, Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin

Planning the workday of bus drivers by a graph list-coloring model

In this work, we address the problem of planning the workday of bus drivers in argentinian intercity bus transport companies. In particular, we focus on a company which needs to fulfill roughly 800 trips per day between 3 cities of the Province of Buenos Aires with a stuff of around 200 drivers and 100 buses. Planning consists of assigning one driver to each trip in a way the driver performs all the trips without scheduling conflicts and minimizing the overall amount of overtime among all bus drivers. We model the problem as a particular Graph Coloring Problem and we propose an Integer Linear Programming formulation. Computations experiments show that this formulation outperforms other ones given in the literature for the same problem. In order to address large instances as the one given by the company, we also propose a heuristic algorithm that delivers better solutions than the company actually uses in a reasonably amount of time. The heuristic has two phases where the first one constructs an initial solution and the second one improves the solution iteratively.Fil: Lucci, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Severin, Daniel Esteban. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentin

A Branch and Price Algorithm for List Coloring Problem

Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.Fil: Lucci, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)Belo HorizonteBrasilCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorConselho Nacional de Desenvolvimento Científico e Técnologico do BrasilUniversidade Federal de Minas Gerai

An integer programming approach for solving a generalized version of the Grundy domination number

A legal dominating sequence of a graph is an ordered dominating set of vertices where each element dominates at least another one not dominated by its predecessors in the sequence. The length of a largest legal dominating sequence is called Grundy domination number. In this work, we introduce a generalized version of the Grundy domination problem. We explicitly calculate the corresponding parameter for paths and web graphs. We propose integer programming formulations for the new problem, find families of valid inequalities and perform extensive computational experiments to compare the formulations as well as to test these inequalities as cuts in a branch-and-cut framework. We also design and evaluate the performance of a heuristic for finding good initial lower and upper bounds and a tabu search that improves the initial lower bound. The test instances include randomly generated graphs, structured graphs, classical benchmark instances and two instances from a real application. Our approach is exact for graphs with 20-50 vertices and provides good solutions for graphs up to 10000 vertices.Fil: Campêlo, Manoel. Universidade Estadual do Ceará; BrasilFil: Severin, Daniel Esteban. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentin

Facets of the polytope of legal sequences

A sequence of vertices in a graph is called a (total) legal dominating sequence if every vertex in the sequence (totally) dominates at least one vertex not dominated by the ones that precedes it, and at the end all vertices of the graph are (totally) dominated. The Grundy (total) domination number of a graph is the size of the largest (total) legal dominating sequence. In this work, we present integer programming formulations for obtaining the Grundy (total) domination number of a graph, we study some aspects of the polyhedral structure of one of them and we test the performance of some new valid inequalities as cuts.Fil: Campêlo, Manoel. Universidade Federal Do Ceará; BrasilFil: Severin, Daniel Esteban. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Development of a new version of "Cordoba Durchmusterung" stellar catalog

En este trabajo se analiza la posibilidad de confeccionar una nueva versión digital del catálogo Córdoba Durchmusterung. Para estimar la misma, se aborda una zona del cielo que comprende alrededor de 18000 estrellas de este catálogo. Se parte de la actual versión digital, disponible en la base de datos VizieR como catálogo I/114, y se corrigen errores de transcripción. Esto se logra generando automáticamente una lista de registros con posibles errores y luego, manualmente, se comparan estos registros del catálogo digital con la versión impresa del mismo. Además, se incorpora información existente en la versión impresa que actualmente no está en la versión digital. Finalmente, se propone un algoritmo que realiza una identificación cruzada entre este catálogo y uno moderno (Positions and Proper Motions eXtended). La particularidad de este algoritmo respecto a los presentes en la literatura es que permite crear referencias cruzadas de estrellas dobles adecuadamente.Fil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ciencias Básicas; ArgentinaFil: Sevilla, Diego Javier Ramón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ciencias Básicas; Argentin

A metaheuristic for crew scheduling in a pickup-and-delivery problem with time windows

A simultaneous vehicle routing and crew scheduling problem (SVRCSP) consists of planning routes for a fleet of vehicles and scheduling their crews, with the particularity that the vehicle–crew correspondence is not fixed through time. This allows a greater planning flexibility and a more efficient use of the fleet, but in counterpart it requires high synchronization. In this work, an SVRCSP is presented, where long-distance pickup-and-delivery requests must be fulfilled over a multiday planning horizon, subject to several constraints such as multiple time windows, hour of services regulation, among others. Crews can be composed of one or two drivers and any of them can be relieved in a given set of locations. Also, they are allowed to travel between locations with noncompany shuttles. The objective is to minimize the cost of travel in company and noncompany vehicles, which depends on the distance, and the penalization for completing requests with delay. A two-stage sequential approach is applied: a set of truck routes is computed in the first stage and a set of driver routes consistent with the previous routes is obtained in the second stage. An algorithm based on the GRASP × ILS metaheuristic, embedded with a repair heuristic to facilitate the construction of initial solutions, is proposed and evaluated for the latter stage. High-quality solutions were found for instances generated with up to 3000 requests and a planning horizon of one to four weeks spread over 15 Argentine cities in less than an hour. Additionally, the possibility of carrying an additional driver reduced the cost of external shuttles by 2.25 times on average compared to individual crews and, in some cases, removed this cost completely.Fil: Lucci, Mauro. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Severin, Daniel Esteban. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Zabala, Paula Lorena. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

An exact DSatur-based algorithm for the Equitable Coloring Problem

This paper describes an exact algorithm for the Equitable Coloring Problem, based on the well known DSatur algorithm for the classic Coloring Problem with new pruning rules specifically derived from the equity constraint. Computational experiences show that our algorithm is competitive with those known in literature.Fil: Méndez Díaz, Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Severin, Daniel Esteban. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Anatomical specializations related to foraging in the visual system of a nocturnal insectivorous bird, the band-winged nightjar (Aves: Caprimulgiformes)

Nocturnal animals that rely on their visual system for foraging, mating, and navigation usually exhibit specific traits associated with living in scotopic conditions. Most nocturnal birds have several visual specializations, such as enlarged eyes and an increased orbital convergence. However, the actual role of binocular vision in nocturnal foraging is still debated. Nightjars (Aves: Caprimulgidae) are predators that actively pursue and capture flying insects in crepuscular and nocturnal environments, mainly using a conspicuous “sit-and-wait” tactic on which pursuit begins with an insect flying over the bird that sits on the ground. In this study, we describe the visual system of the band-winged nightjar (Systellura longirostris), with emphasis on anatomical features previously described as relevant for nocturnal birds. Orbit convergence, determined by 3D scanning of the skull, was 73.28°. The visual field, determined by ophthalmoscopic reflex, exhibits an area of maximum binocular overlap of 42°, and it is dorsally oriented. The eyes showed a nocturnal-like normalized corneal aperture/axial length index. Retinal ganglion cells (RGCs) were relatively scant, and distributed in an unusual oblique-band pattern, with higher concentrations in the ventrotemporal quadrant. Together, these results indicate that the band-winged nightjar exhibits a retinal specialization associated with the binocular area of their dorsal visual field, a relevant area for pursuit triggering and prey attacks. The RGC distribution observed is unusual among birds, but similar to that of some visually dependent insectivorous bats, suggesting that those features might be convergent in relation to feeding strategies