Bounded coloring of co-comparability graphs and the pickup and delivery tour combination problem

• Autores: Bonomo, Flavia; Mattia, Sara; Oriolo, Gianpaolo
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Bounded Coloring; Capacitated Coloring; Equitable Coloring; Permutation Graphs; Scheduling Problems; Thinness
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

The Double Traveling Salesman Problem with Multiple Stacks is a vehicle routing problem in which pickups and deliveries must be performed in two independent networks. The items are stored in stacks and repacking is not allowed. Given a pickup and a delivery tour, the problem of checking if there exists a valid distribution of items into s stacks of size h that is consistent with the given tours, is known as Pickup and Delivery Tour Combination (PDTC) problem. n the paper, we show that the PDTC problem can be solved in polynomial time when the number s of stacks is fixed but the size of each stack is not. We build upon the equivalence between the PDTC problem and the bounded coloring (BC) problem on permutation graphs: for the latter problem, s is the number of colors and h is the number of vertices that can get a same color. We show that the BC problem can be solved in polynomial time when s is a fixed constant on co-comparability graphs, a superclass of permutation graphs. To the contrary, the BC problem is known to be hard on permutation graphs when h≥ 6 is a fixed constant, but s is unbounded.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Mattia, Sara. Technische Universität Dortmund; Alemania
Fil: Oriolo, Gianpaolo. Universita Tor Vergata; Italia