Digraph Coloring Games and Game-Perfectness

In this thesis the game chromatic number of a digraph is introduced as a game-theoretic variant of the dichromatic number. This notion generalizes the well-known game chromatic number of a graph. An extended model also takes into account relaxed colorings and asymmetric move sequences. Game-perfectness is defined as a game-theoretic variant of perfectness of a graph, and is generalized to digraphs. We examine upper and lower bounds for the game chromatic number of several classes of digraphs. In the last part of the thesis, we characterize game-perfect digraphs with small clique number, and prove general results concerning game-perfectness. Some results are verified with the help of a computer program that is discussed in the appendix

Game Theoretical Approaches for Wireless Networks

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 김성철.In this dissertation, I introduce three algorithms, which are connectivity reconstruction game (CRG), adaptive sector coloring game (ASCG), and asymmetric transmission game (ATG), by mainly using supermodular game and exact potential game with considerations of various objectives (e.g., energy consumption and interference management) in wireless sensor and cellular networks. My main contributions are threefold: 1) connectivity relaxation (energy saving) in wireless localization2) intercell interference coordination in wireless cellular networks3) interference minimization in wireless ad-hoc relay networks. The corresponding explanations are as follows. 1) In geographically dense and energy limited wireless sensor networks, connectivity based localization with full power transmission can be inefficient in terms of energy consumption. In this work, I propose a distributed power control based connectivity reconstruction game, which takes into considerations of both energy efficiency and the quality of localization. The proposed scheme results in a better performance with an improved 61.9% reduction in energy consumption while maintaining the performance of localization at a level similar to the conventional algorithm with full power transmission. 2) Inter-cell interference coordination (ICIC) is a promising technique to improve the performance of frequency-domain packet scheduling (FDPS) in downlink LTE/LTEA networks. However, it is difficult to maximize the performance of FDPS using static ICIC schemes because of insufficient consideration of signal-to-interference-and-noise ratio (SINR) distribution and user fairness. On the other hand, dynamic ICIC schemes based on channel state information (CSI) also have difficulty presented in the excessive signaling overhead and X2 interface latency. In order to overcome these drawbacks, I introduce a new concept of ICIC problem based on geometric network information (GNI) and propose an ASCG as a decentralized solution of the GNI based ICIC problem. Furthermore, I develop an ASCG with a dominant strategy space noted as ASCGD to secure a stable solution through proving the existence of Nash equilibrium (NE). The proposed scheme provides better performance in terms of system throughput gain of up to about 44.1%, and especially of up to about 221% for the worst 10% users than static ICIC schemes. Moreover, the performance of the CSI based ICIC, which require too much computational load and signaling overhead, is only 13.0% and 5.6% higher than that of ASCG-D regarding the total user throughput and the worst 10% user throughput, respectively. The most interesting outcome is that the signaling overhead of ASCG-D is 1/144 of dynamic ICIC schemes one. 3) In this work, I introduce the new concept of temporal diversity utilization based on asymmetric transmission to minimize network interference in wireless ad-hoc networks with a two-hop half-duplex relaying (HDR) protocol. Asymmetric transmission is an interference-aware backoff technique, in which each communication session (source-relay-destination link) adaptively chooses a certain subset of spectrallyorthogonal data streaming which should be delayed by the duration of one time-slot (i.e., half of one subframe). I design the problem in the HDR scenario by applying the concept of asymmetric transmission, and evaluate the game-theoretical algorithm, called ATG, to derive the suboptimal solution. I show that ATG is an exact potential game, and derive its convergence and optimality properties. Furthermore, I develop an approximated version of ATG (termed A-ATG) in order to reduce signaling and computational complexity. Numerical results verify that two algorithms proposed showsignificant synergistic effects when collaborating with the conventional methods in terms of interference coordination. Ultimately, the energy consumption to satisfy the rate requirement is reduced by up to 17:4% compared to the conventional schemes alone.1 INTRODUCTION 1 1.1 Application of Supermodular Game for Connectivity Relaxation in Wireless Localization 2 1.2 Application of Exact Potential Game for Effective Inter-Cell Interference Coordination in Wireless Cellular Networks 3 1.3 Application of Exact Potential Game for Interference Minimization in Wireless Ad-hoc Relay Networks 7 1.4 Dissertation Outline 11 2 APPLICATION OF SUPERMODULAR GAME: Distributed Power Control based Connectivity Reconstruction Game inWireless Localization 13 2.1 Brief Introduction 13 2.2 System Model 13 2.3 Proposed Power Control Algorithm 14 2.3.1 Reliability Function 14 2.3.2 Game Formulation 15 2.3.3 Convergence Properties of CRG 17 2.4 Simulation Results 20 3 APPLICATION OF EXACT POTENTIAL GAME: Adaptive Sector Coloring Game for Geometric Network Information based Inter-Cell Interference Coordination in Wireless Cellular Networks 24 3.1 Brief Introduction 24 3.2 Network Model 26 3.2.1 System Preliminaries 26 3.2.2 Determination of Time Policy 27 3.2.3 Two-Stage Framework of RB Allocation 27 3.3 PROBLEM FORMULATION: Geometric Network Information based ICIC 28 3.3.1 Outline 28 3.3.2 What Is the GNI 28 3.3.3 Temporal Perspective: Why GNI 29 3.3.4 Spatial Perspective: How do I Design a Suitable Utility Function 29 3.3.5 GNI based ICIC Problem 33 3.4 ADAPTIVE SECTOR COLORING GAME 33 3.4.1 Design of ASCG 33 3.4.2 ASCG with a Dominant Strategy Space 35 3.4.3 Summary of System Operation 40 3.5 PERFORMANCE EVALUATION 41 3.5.1 Simulation Settings and Baselines for Comparison 41 3.5.2 SINR Distribution and Average User Throughput 43 3.5.3 Signaling Overhead for ICIC and FDPS 47 3.5.4 Reduction of Feasible ASCG Strategy Space 49 4 APPLICATION OF EXACT POTENTIAL GAME: Asymmetric Transmission Game for Interference Coordination in Wireless Ad-hoc Relay Networks 51 4.1 Brief Introduction 51 4.2 Problem Formulation 52 4.2.1 System Preliminaries 52 4.2.2 The Concept of Asymmetric Transmission for Interference Coordination: A Simple Example 53 4.2.3 Optimization Problem 54 4.3 Asymmetric Transmission Game 55 4.3.1 Game Formulation 55 4.3.2 Convergence and Optimality Properties of Asymmetric Transmission Game 55 4.3.3 Approximated Version of Asymmetric Transmission Game . . 58 4.4 Simulation Results 61 4.4.1 Parameters Settings 61 4.4.2 Network Interference in One-shot Game 62 4.4.3 Individual Power Consumption in One-shot Game 66 4.4.4 Total Energy Consumption in 1000-shot Games 70 4.4.5 Complexity Analysis for Varying K and M 71 5 CONCLUSION 74 Appendix A Derivation of number of partitions for extracting the dominant feasible strategy set 76 Appendix B Derivation of the cardinal number of the dominant feasible strategy set 78 Appendix C Existence of NE in ASCG-D 79 Appendix D The Required Signaling overhead of ASCG-D 82 Bibliography 83 Abstract (In Korean) 93Docto

Refined activation strategy for the marking game

AbstractThis paper introduces a new strategy for playing the marking game on graphs. Using this strategy, we prove that if G is a planar graph, then the game colouring number of G, and hence the game chromatic number of G, is at most 17

Distributed radio resource allocation in wireless heterogeneous networks

This dissertation studies the problem of resource allocation in the radio access network of heterogeneous small-cell networks (HetSNets). A HetSNet is constructed by introducing smallcells(SCs) to a geographical area that is served by a well-structured macrocell network. These SCs reuse the frequency bands of the macro-network and operate in the interference-limited region. Thus, complex radio resource allocation schemes are required to manage interference and improve spectral efficiency. Both centralized and distributed approaches have been suggested by researchers to solve this problem. This dissertation follows the distributed approach under the self-organizing networks (SONs) paradigm. In particular, it develops game-theoretic and learning-theoretic modeling, analysis, and algorithms. Even though SONs may perform subpar to a centralized optimal controller, they are highly scalable and fault-tolerant. There are many facets to the problem of wireless resource allocation. They vary by the application, solution, methodology, and resource type. Therefore, this thesis restricts the treatment to four subproblems that were chosen due to their significant impact on network performance and suitability to our interests and expertise. Game theory and mechanism design are the main tools used since they provide a sufficiently rich environment to model the SON problem. Firstly, this thesis takes into consideration the problem of uplink orthogonal channel access in a dense cluster of SCs that is deployed in a macrocell service area. Two variations of this problem are modeled as noncooperative Bayesian games and the existence of pure-Bayesian Nash symmetric equilibria are demonstrated. Secondly, this thesis presents the generalized satisfaction equilibrium (GSE) for games in satisfaction-form. Each wireless agent has a constraint to satisfy and the GSE is a mixed-strategy profile from which no unsatisfied agent can unilaterally deviate to satisfaction. The objective of the GSE is to propose an alternative equilibrium that is designed specifically to model wireless users. The existence of the GSE, its computational complexity, and its performance compared to the Nash equilibrium are discussed. Thirdly, this thesis introduces verification mechanisms for dynamic self-organization of Wireless access networks. The main focus of verification mechanisms is to replace monetary transfers that are prevalent in current research. In the wireless environment particular private information of the wireless agents, such as block error rate and application class, can be verified at the access points. This verification capability can be used to threaten false reports with backhaul throttling. The agents then learn the truthful equilibrium over time by observing the rewards and punishments. Finally, the problem of admission control in the interfering-multiple access channel with rate constraints is addressed. In the incomplete information setting, with compact convex channel power gains, the resulting Bayesian game possesses at least one pureBayesian Nash equilibrium in on-off threshold strategies. The above-summarized results of this thesis demonstrate that the HetSNets are amenable to self-organization, albeit with adapted incentives and equilibria to fit the wireless environment. Further research problems to expand these results are identified at the end of this document

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Exploiting Structure In Combinatorial Problems With Applications In Computational Sustainability

Combinatorial decision and optimization problems are at the core of many tasks with practical importance in areas as diverse as planning and scheduling, supply chain management, hardware and software verification, electronic commerce, and computational biology. Another important source of combinatorial problems is the newly emerging field of computational sustainability, which addresses decision-making aimed at balancing social, economic and environmental needs to guarantee the long-term prosperity of life on our planet. This dissertation studies different forms of problem structure that can be exploited in developing scalable algorithmic techniques capable of addressing large real-world combinatorial problems. There are three major contributions in this work: 1) We study a form of hidden problem structure called a backdoor, a set of key decision variables that captures the combinatorics of the problem, and reveal that many real-world problems encoded as Boolean satisfiability or mixed-integer linear programs contain small backdoors. We study backdoors both theoretically and empirically and characterize important tradeoffs between the computational complexity of finding backdoors and their effectiveness in capturing problem structure succinctly. 2) We contribute several domain-specific mathematical formulations and algorithmic techniques that exploit specific aspects of problem structure arising in budget-constrained conservation planning for wildlife habitat connectivity. Our solution approaches scale to real-world conservation settings and provide important decision-support tools for cost-benefit analysis. 3) We propose a new survey-planning methodology to assist in the construction of accurate predictive models, which are especially relevant in sustainability areas such as species- distribution prediction and climate-change impact studies. In particular, we design a technique that takes advantage of submodularity, a structural property of the function to be optimized, and results in a polynomial-time procedure with approximation guarantees