Metric properties of large graphs

Guillaume Ducoffe 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Large scale communication networks are everywhere, ranging from data centers withmillions of servers to social networks with billions of users. This thesis is devoted tothe fine-grained complexity analysis of combinatorial problems on these networks.In the first part, we focus on the embeddability of communication networks totree topologies. This property has been shown to be crucial in the understandingof some aspects of network traffic (such as congestion). More precisely, we studythe computational complexity of Gromov hyperbolicity and of tree decompositionparameters in graphs – including treelength and treebreadth. On the way, we givenew bounds on these parameters in several graph classes of interest, some of thembeing used in the design of data center interconnection networks. The main resultin this part is a relationship between treelength and treewidth: another well-studiedgraph parameter, that gives a unifying view of treelikeness in graphs and has algorithmicapplications. This part borrows from graph theory and recent techniques incomplexity theory. The second part of the thesis is on the modeling of two privacy concerns with social networking services. We aim at analysing information flows in these networks,represented as dynamical processes on graphs. First, a coloring game on graphs isstudied as a solution concept for the dynamic of online communities. We give afine-grained complexity analysis for computing Nash and strong Nash equilibria inthis game, thereby answering open questions from the literature. On the way, wepropose new directions in algorithmic game theory and parallel complexity, usingcoloring games as a case example
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  • HAL Id : tel-01485328, version 1



Guillaume Ducoffe. Metric properties of large graphs. Other [cs.OH]. Université Côte d'Azur, 2016. English. ⟨NNT : 2016AZUR4134⟩. ⟨tel-01485328⟩



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