On fair cost facility location games with non-singleton players

In the fair cost facility location game, players control terminals and must open and connect each terminal to a facility, while paying connection costs and equally sharing the opening costs associated with the facilities it connects to. In most of the literature, it is assumed that each player control a single terminal. We explore a more general version of the game where each player may control multiple terminals. We prove that this game does not always possess pure Nash equilibria, and deciding whether an instance has equilibria is NP-Hard, even in metric instances. Furthermore, we present results regarding the efficiency of equilibria, showing that the price of stability of this game is equal to the price of anarchy, in both uncapacitated and capacitated settings

Stealthy River Navigation in Jungle Combat Conditions

One of the biggest challenges for Brazilian military logisticians is to support effective jungle warfare for both real and training operations carried out by their combat forces in the Amazonian region. The jungle\u27s heat, humidity, and dense vegetation put significant demands on the supply chain. Further, because of the difficulties of land or air transportation, water transport is the most reasonable transportation option to sustain these deployed forces. Planners must select from among the available watercourses those whose surroundings provide stealthy navigation to the combat force location where the requested supplies can be safely unloaded. We seek a method of determining a path through a river network that blends short transit times with maximal shade coverage from forest growth along the riverbanks. We combine an astronomical algorithm for computing shadow coverage with Dijkstra\u27s shortest path algorithm to determine the start time and routing information necessary for a supply boat to travel from a depot to a resupply point that minimizes weighted risk, which is defined as the product of shade coverage and arc transit time

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Shortest Route at Dynamic Location with Node Combination-Dijkstra Algorithm

Abstract— Online transportation has become a basic requirement of the general public in support of all activities to go to work, school or vacation to the sights. Public transportation services compete to provide the best service so that consumers feel comfortable using the services offered, so that all activities are noticed, one of them is the search for the shortest route in picking the buyer or delivering to the destination. Node Combination method can minimize memory usage and this methode is more optimal when compared to A* and Ant Colony in the shortest route search like Dijkstra algorithm, but can’t store the history node that has been passed. Therefore, using node combination algorithm is very good in searching the shortest distance is not the shortest route. This paper is structured to modify the node combination algorithm to solve the problem of finding the shortest route at the dynamic location obtained from the transport fleet by displaying the nodes that have the shortest distance and will be implemented in the geographic information system in the form of map to facilitate the use of the system. Keywords— Shortest Path, Algorithm Dijkstra, Node Combination, Dynamic Location (key words

Jogos de localização de instalações não cooperativos e percepção de custos

Orientadores: Eduardo Candido Xavier, Guido SchäferTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Esta tese de doutorado cobre a interseção entre problemas de localização de instalações e teoria dos jogos algorítmica não cooperativa, com ênfase em alterações da percepção de custos de cada jogador e seu efeito na qualidade de equilíbrios. O problema de localização de instalações é um dos problemas fundamentais em otimização combinatória. Em sua versão clássica, existe um conjunto de terminais e um conjunto de instalações, e cada terminal necessita ser conectado a uma instalação, para que esta providencie bens ou serviços. O objetivo é minimizar o total dos custos associados à abertura das instalações e à conexão dos terminais a essas instalações. Na prática, existem diversos cenários onde é inviável ou não é desejável que uma autoridade central única decida como clientes devem escolher as instalações às quais se conectam. Dessa forma, é importante estudar como a independência desses terminais pode afetar a eficiência social e a complexidade computacional para esses cenários. A teoria dos jogos algorítmica pode ser útil para tais cenários, em particular sua parte não cooperativa. A teoria dos jogos algorítmica preenche uma lacuna entre a ciência da computação teórica e a teoria dos jogos, e está interessada em questões como a complexidade computacional de se encontrar equilíbrios, o quanto o bem-estar social pode ser perdido devido ao egoísmo de jogadores e como desenvolver mecanismos para garantir que o melhor interesse dos jogadores se alinhe com o ótimo social. Nesta tese, estudamos jogos de localização de instalações não cooperativos e algumas de suas variantes. Focamos em responder questões relativas à existência de equilíbrios de Nash puros e sobre as principais medidas de perda de eficiência, o preço da anarquia e preço da estabilidade. Apresentamos uma revisão das descobertas mais importantes para as variantes básicas, com novos resultados nos casos onde nenhum era conhecido. Para a versão capacitada desses jogos, mostramos que, enquanto a simultaneidade pode levar a uma perda de eficiência ilimitada, quando se admite a sequencialidade de jogadores, é possível mostrar que a perda de eficiência tem limites. Também investigamos como mudanças na percepção de custo podem afetar a qualidade de equilíbrios de duas maneiras: através de jogadores altruístas e de esquemas de taxação. No primeiro, adaptamos resultados de jogos de compartilhamento justo de custos e apresentamos novos resultados sobre uma versão sem regras de compartilhamento. No último, propomos um modelo de mudança na percepção de custos, onde os jogadores consideram um pedágio adicional em suas conexões ao calcular seus custos. Apresentamos limitantes para o custo total das taxas no problema de pedágios mínimos, onde o objetivo é encontrar o valor mínimo de pedágio necessário para garantir que um determinado perfil de estratégia socialmente ótimo seja escolhido pelos jogadores. Mostramos algoritmos para encontrar pedágios ótimos para tal problema em casos especiais e relacionamos esse problema a um problema de emparelhamento NP-difícilAbstract: This Ph.D. thesis covers the intersection between facility location problems and non-cooperative algorithmic game theory, with emphasis on possible changes in cost perception and its effects in regards to quality of equilibria. The facility location problem is one of the fundamental problems in the combinatorial optimization field of study. In its classic version, there exists a set of terminals and a set of facilities, and each terminal must be connected to a facility, in order for goods or services to be provided. The objective is to minimize the total costs associated with opening the facilities and connecting all the terminals to these facilities. In practice, there are multiple scenarios where it is either infeasible or not desirable for a single central authority to decide which facilities terminals connect to. Thus, it is important to study how the independence of these terminals may affect social efficiency and computational complexity in these scenarios. For this analysis algorithmic game theory can be of use, in particular its non-cooperative part. Algorithmic game theory bridges a gap between theoretical computer science and game theory, and is interested in questions such as how hard it is computationally to find equilibria, how much social welfare can be lost due to player selfishness and how to develop mechanisms to ensure that players' best interest align with the social optimum. In this thesis we study non-cooperative facility location games and several of its variants. We focus on answering the questions concerning the existence of pure Nash equilibria and the main measures of efficiency loss, the price of anarchy and the price of stability. We present a review of the most important findings for the basic variants and show new results where none were known. For the capacitated version of these games, we show that while simultaneity may lead to unbounded loss of efficiency, when sequentiality is allowed, it is possible to bound the efficiency loss. We also investigate how changes in players' perception of cost can affect the efficiency loss of these games in two ways: through altruistic players and through tolling schemes. In the former we adapt results from fair cost sharing games and present new results concerning a version with no cost sharing rules. In the latter, we propose a model for change in cost perception where players consider an additional toll in their connections when calculating their best responses. We present bounds for total toll cost in the minimum toll problem, where the objective is to find the minimum amount of tolls needed to ensure that a certain socially optimal strategy profile will be chosen by players. We show algorithms for finding optimal tolls for the minimum toll problem in special cases and provide some insight into this problem by connecting it to a matching problem which we prove is NP-hardDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação147141/2016-8CAPESCNP