Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c

Dynamic Fairness-Aware Spectrum Auction for Enhanced Licensed Shared Access in 6G Networks

This article introduces a new approach to address the spectrum scarcity challenge in 6G networks by implementing the enhanced licensed shared access (ELSA) framework. Our proposed auction mechanism aims to ensure fairness in spectrum allocation to mobile network operators (MNOs) through a novel weighted auction called the fair Vickery-Clarke-Groves (FVCG) mechanism. Through comparison with traditional methods, the study demonstrates that the proposed auction method improves fairness significantly. We suggest using spectrum sensing and integrating UAV-based networks to enhance efficiency of the LSA system. This research employs two methods to solve the problem. We first propose a novel greedy algorithm, named market share based weighted greedy algorithm (MSWGA) to achieve better fairness compared to the traditional auction methods and as the second approach, we exploit deep reinforcement learning (DRL) algorithms, to optimize the auction policy and demonstrate its superiority over other methods. Simulation results show that the deep deterministic policy gradient (DDPG) method performs superior to soft actor critic (SAC), MSWGA, and greedy methods. Moreover, a significant improvement is observed in fairness index compared to the traditional greedy auction methods. This improvement is as high as about 27% and 35% when deploying the MSWGA and DDPG methods, respectively.Comment: 13 pages, 11 figure

A maximal covering location problem based optimization of complex processes : a novel computational approach

Esta tesis basada en artículos analiza un nuevo enfoque computacional para el problema de localización de cobertura máxima (MCLP, sigla en inglés). Consideramos una formulación de tipo difuso del MCLP genérico y desarrollamos los aspectos teóricos y numéricos necesarios del Método de Separación (SM) propuesto. Una estructura específica del MCLP originalmente dado hace posible reducirlo a dos problemas auxiliares de tipo mochila (Knapsack). La separación equivalente que proponemos reduce esencialmente la complejidad de los algoritmos resultantes. Este algoritmo también incorpora una técnica de relajación convencional y el método de escalarización aplicado a un problema auxiliar de optimización multiobjetivo. La metodología de solución propuesta se aplica a continuación a la optimización de la cadena de suministro en presencia de información incompleta. Estudiamos dos ejemplos ilustrativos y realizamos un análisis riguroso de los resultados obtenidos.This Ph.D. article-based thesis discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A speci_c structure of the originally given MCLP makes it possible to reduce it to two auxiliary Knapsack-type problems. The equivalent separation we propose reduces essentially the complexity of the resulting computational algorithms. This algorithm also incorporates a conventional relaxation technique and the scalarizing method applied to an auxiliary multiobjective optimization problem. The proposed solution methodology is next applied to Supply Chain optimization in the presence of incomplete information. We study two illustrative examples and give a rigorous analysis of the obtained results.Doctor en Modelación y Computación CientíficaDoctorad