23 research outputs found

    Using coalitional games on biological networks to measure centrality and power of genes

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    Abstract Motivation: The interpretation of gene interaction in biological networks generates the need for a meaningful ranking of network elements. Classical centrality analysis ranks network elements according to their importance but may fail to reflect the power of each gene in interaction with the others. Results: We introduce a new approach using coalitional games to evaluate the centrality of genes in networks keeping into account genes' interactions. The Shapley value for coalitional games is used to express the power of each gene in interaction with the others and to stress the centrality of certain hub genes in the regulation of biological pathways of interest. The main improvement of this contribution, with respect to previous applications of game theory to gene expression analysis, consists in a finer resolution of the gene interaction investigated in the model, which is based on pairwise relationships of genes in the network. In addition, the new approach allows for the integration of a priori knowledge about genes playing a key function on a certain biological process. An approximation method for practical computation on large biological networks, together with a comparison with other centrality measures, is also presented. Contact: [email protected]

    Network partitioning algorithms as cooperative games

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    International audienceThe paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolutions. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for approaches based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling

    Structural and computational aspects of simple and influence games

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    Simple games are a fundamental class of cooperative games. They have a huge relevance in several areas of computer science, social sciences and discrete applied mathematics. The algorithmic and computational complexity aspects of simple games have been gaining notoriety in the recent years. In this thesis we review different computational problems related to properties, parameters, and solution concepts of simple games. We consider different forms of representation of simple games, regular games and weighted games, and we analyze the computational complexity required to transform a game from one representation to another. We also analyze the complexity of several open problems under different forms of representation. In this scenario, we prove that the problem of deciding whether a simple game in minimal winning form is decisive (a problem that is associated to the duality problem of hypergraphs and monotone Boolean functions) can be solved in quasi-polynomial time, and that this problem can be polynomially reduced to the same problem but restricted to regular games in shift-minimal winning form. We also prove that the problem of deciding wheter a regular game is strong in shift-minimal winning form is coNP-complete. Further, for the width, one of the parameters of simple games, we prove that for simple games in minimal winning form it can be computed in polynomial time. Regardless of the form of representation, we also analyze counting and enumeration problems for several subfamilies of these games. We also introduce influence games, which are a new approach to study simple games based on a model of spread of influence in a social network, where influence spreads according to the linear threshold model. We show that influence games capture the whole class of simple games. Moreover, we study for influence games the complexity of the problems related to parameters, properties and solution concepts considered for simple games. We consider extremal cases with respect to demand of influence, and we show that, for these subfamilies, several problems become polynomial. We finish with some applications inspired on influence games. The first set of results concerns to the definition of collective choice models. For mediation systems, several of the problems of properties mentioned above are polynomial-time solvable. For influence systems, we prove that computing the satisfaction (a measure equivalent to the Rae index and similar to the Banzhaf value) is hard unless we consider some restrictions in the model. For OLFM systems, a generalization of OLF systems (van den Brink et al. 2011, 2012) we provide an axiomatization of satisfaction. The second set of results concerns to social network analysis. We define new centrality measures of social networks that we compare on real networks with some classical centrality measures.Los juegos simples son una clase fundamental de juegos cooperativos, que tiene una enorme relevancia en diversas áreas de ciencias de la computación, ciencias sociales y matemáticas discretas aplicadas. En los últimos años, los distintos aspectos algorítmicos y de complejidad computacional de los juegos simples ha ido ganando notoriedad. En esta tesis revisamos los distintos problemas computacionales relacionados con propiedades, parámetros y conceptos de solución de juegos simples. Primero consideramos distintas formas de representación de juegos simples, juegos regulares y juegos de mayoría ponderada, y estudiamos la complejidad computacional requerida para transformar un juego desde una representación a otra. También analizamos la complejidad de varios problemas abiertos bajo diferentes formas de representación. En este sentido, demostramos que el problema de decidir si un juego simple en forma ganadora minimal es decisivo (un problema asociado al problema de dualidad de hipergrafos y funciones booleanas monótonas) puede resolverse en tiempo cuasi-polinomial, y que este problema puede reducirse polinomialmente al mismo problema pero restringido a juegos regulares en forma ganadora shift-minimal. También demostramos que el problema de decidir si un juego regular en forma ganadora shift-minimal es fuerte (strong) es coNP-completo. Adicionalmente, para juegos simples en forma ganadora minimal demostramos que el parámetro de anchura (width) puede computarse en tiempo polinomial. Independientemente de la forma de representación, también estudiamos problemas de enumeración y conteo para varias subfamilias de juegos simples. Luego introducimos los juegos de influencia, un nuevo enfoque para estudiar juegos simples basado en un modelo de dispersión de influencia en redes sociales, donde la influencia se dispersa de acuerdo con el modelo de umbral lineal (linear threshold model). Demostramos que los juegos de influencia abarcan la totalidad de la clase de los juegos simples. Para estos juegos también estudiamos la complejidad de los problemas relacionados con parámetros, propiedades y conceptos de solución considerados para los juegos simples. Además consideramos casos extremos con respecto a la demanda de influencia, y probamos que para ciertas subfamilias, varios de estos problemas se vuelven polinomiales. Finalmente estudiamos algunas aplicaciones inspiradas en los juegos de influencia. El primer conjunto de estos resultados tiene que ver con la definición de modelos de decisión colectiva. Para sistemas de mediación, varios de los problemas de propiedades mencionados anteriormente son polinomialmente resolubles. Para los sistemas de influencia, demostramos que computar la satisfacción (una medida equivalente al índice de Rae y similar al valor de Banzhaf) es difícil a menos que consideremos algunas restricciones en el modelo. Para los sistemas OLFM, una generalización de los sistemas OLF (van den Brink et al. 2011, 2012) proporcionamos una axiomatización para la medida de satisfacción. El segundo conjunto de resultados se refiere al análisis de redes sociales, y en particular con la definición de nuevas medidas de centralidad de redes sociales, que comparamos en redes reales con otras medidas de centralidad clásica

    Responsibility and verification: Importance value in temporal logics

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    We aim at measuring the influence of the nondeterministic choices of a part of a system on its ability to satisfy a specification. For this purpose, we apply the concept of Shapley values to verification as a means to evaluate how important a part of a system is. The importance of a component is measured by giving its control to an adversary, alone or along with other components, and testing whether the system can still fulfill the specification. We study this idea in the framework of model-checking with various classical types of linear-time specification, and propose several ways to transpose it to branching ones. We also provide tight complexity bounds in almost every case.Comment: 22 pages, 12 figure

    Constraint Optimisation Techniques for Real-World Applications

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    Constraint optimisation represents a fundamental technique that has been successfully employed in Multi-Agent Systems (MAS) in order to face a number of multi-agent coordination challenges. In this thesis we focus on Coalition Formation (CF), one of the key approaches for coordination in MAS. CF aims at the formation of groups that maximise a particular objective functions (e.g., arrange shared rides among multiple agents in order to minimise travel costs). Specifically, we discuss a special case of CF known as Graph-Constrained CF (GCCF) where a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. In particular, the contributions of this thesis are the following. We propose a novel representation of this problem and we design an efficient solution algorithm, i.e., CFSS. We evaluate CFSS on GCCF scenarios like collective energy purchasing and social ridesharing using realistic data (i.e., energy consumption profiles from households in the UK, GeoLife for spatial data, and Twitter as social network). Results show that CFSS outperforms state of the art GCCF approaches both in terms of runtime and scalability. CFSS is the first algorithm that provides solutions with good quality guarantees for large-scale GCCF instances with thousands of agents (i.e., more that 2700). In addition, we address the problem of computing the transfer or payment to each agent to ensure it is fairly rewarded for its contribution to its coalition. This aspect of CF, denoted as payment computation, is of utmost importance in scenario characterised by agents with rational behaviours, such as collective energy purchasing and social ridesharing. In this perspective, we propose PK, the first method to compute payments in large-scale GCCF scenarios that are also stable in a game-theoretic sense. Finally, we provide an alternative method for the solution of GCCF, by exploiting the close relation between such problem and Constraint Optimisation Problems (COPs). We consider Bucket Elimination (BE), one of the most important algorithmic frameworks to solve COPs, and we propose CUBE, a highly-parallel GPU implementation of the most computationally intensive operations of BE. CUBE adopts an efficient memory layout that results in a high computational throughput. In addition, CUBE is not limited by the amount of memory of the GPU and, hence, it can cope with problems of realistic nature. CUBE has been tested on the SPOT5 dataset, which contains several satellite management problems modelled as COPs. Moreover, we use CUBE to solve COP-GCCF, the first COP formalisation of GCCF that results in a linear number of constraints with respect to the number of agents. This property is crucial to ensure the scalability of our approach. Results show that COP-GCCF produces significant improvements with respect to state of the art algorithms when applied to a realistic graph topology (i.e., Twitter), both in terms of runtime and memory. Overall, this thesis provides a novel perspective on important techniques in the context of MAS (such as CF and constraint optimisation), allowing to solve realistic problems involving thousands of agents for the first time
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