Topological Price of Anarchy bounds for clustering games on networks

We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their choices with their neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs, which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds

Graph Algorithms and Applications

The mixture of data in real-life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. This book contains some papers reporting recent achievements regarding graph models, algorithms, and applications to problems in the real world, with some focus on optimization and computational complexity

The Influence of Structure in Supply and Demand on the Performance Characteristics of Road Traffic Networks: An exploration of how methodological approaches from network science can be implemented for a transportation research problem

Recently, researchers in the field of Network Science have begun to study how the structural properties of road traffic networks affect their performance characteristics. An understanding of how different structures of network infrastructure and travel demand combine to yield different performance characteristics would be useful because it could help identify how existing road traffic networks could be used more effectively or how structural features, which yield desirable performance characteristics, could be built into the construction of new road traffic networks. Thus far, however, these studies have been restricted to numerical experiments with synthetic networks that do not provide plausible representations of real road traffic networks. Furthermore, these studies have used a disparate range of parameter settings for supply and demand structure, making it difficult to generalise their findings, and have provided no explanations for their conclusions. To address these deficiencies, this thesis proposes an investigative framework for studying the effects of structure on the performance characteristics of road traffic networks. This framework comprises an experimental part, which describes how to design and conduct numerical experiments so as to provide useful insights into how performance varies with respect to specific aspects of network structure; and an analytical part, which focuses on developing explanations for patterns uncovered numerically. This thesis then demonstrates the application of this framework to an investigation of how two performance indicators; the average link Volume-to-Capacity ratio and the Price of Anarchy, vary with respect to four aspects of road traffic network structure. As part of this investigation, a simple model of road network generation is presented that produces spectrums of plausible, synthetic road traffic network ensembles, which vary with respect to specific aspects of structure. Focussing on the variation of the Price of Anarchy with travel demand, this thesis then establishes theory that explains several features of the variation shown numerically

A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th