Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the listcoloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs where the former admits polynomial-time algorithms but the latter is NP-complete. Our goal is to analyze the computational complexity of coloring problems lying "between" (from a computational complexity viewpoint) these two problems: precoloring extension, μ-coloring, and (γ , μ)-coloring.
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.
The Full Strategy Minority Game (FSMG) is an instance of the Minority Game
(MG) which includes a single copy of every potential agent. In this work, we
explicitly solve the FSMG thanks to certain symmetries of this game.
Furthermore, by considering the MG as a statistical sample of the FSMG, we
compute approximated values of the key variable {\sigma}2/N in the symmetric
phase for different versions of the MG. As another application we prove that
our results can be easily modified in order to handle certain kind of initial
biased strategies scores, in particular when the bias is introduced at the
agents' level. We also show that the FSMG verifies a strict period two dynamics
(i.e., period two dynamics satisfied with probability 1) giving, to the best of
our knowledge, the first example of an instance of the MG for which this
feature can be analytically proved. Thanks to this property, it is possible to
compute in a simple way the probability that a general instance of the MG
breaks the period two dynamics for the first time in a given simulation.Comment: To appear in Physica
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 $200,000 per year in addition to the qualitative impacts of less traffic disruption, less vehicle driver fatigue and less pollution.
Artículo de publicación ISIShip 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
Point-to-Multipoint systems are a kind of radio systems supplying wireless access to voice/data communication networks. Such systems have to be run using a certain frequency spectrum, which typically causes capacity problems. Hence it is, on the one hand, necessary to reuse frequencies but, on the other hand, no interference must be caused thereby. This leads to a combinatorial optimization problem, the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-hard and it is known that, for these problems, there exist no polynomial time algorithms with a fixed approximation ratio. Algorithms based on cutting planes have shown to be successful for many other combinatorial optimization problems. In order to apply such methods, knowledge on the associated polytopes is required. The present paper contributes to this issue, exploring basic properties of chromatic scheduling polytopes and several classes of facet-defining inequalities.
Keywords Bandwidth allocation . Polyhedral combinatoricsPoint-to-Multipoint Radio Access Systems (PMP-Systems) are a kind of radio systems supplying wireless access to voice/data communication networks. Base stations form the access points to the backbone network; customer terminals are linked to the base stations by means of radio signals. Some specific part of the radio frequency spectrum has to be used only to J. L.
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