Graphs And Algorithms In Communication Networks

Algorithmic discrete mathematics plays a key role in the development of information and communication technologies, and methods that arise in computer science, mathematics and operations research – in particular in algorithms, computational complexity, distributed computing and optimization – are vital to modern services such as mobile telephony, online banking and VoIP. This book examines communication networking from a mathematical viewpoint. The contributing authors took part in the European COST action 293 – a four-year program of multidisciplinary research on this subject. In this book they offer introductory overviews and state-of-the-art assessments of current and future research in the fields of broadband, optical, wireless and ad hoc networks. Particular topics of interest are design, optimization, robustness and energy consumption. The book will be of interest to graduate students, researchers and practitioners in the areas of networking, theoretical computer science, operations research, distributed computing and mathematics.

Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed

This book presents a comprehensive review of key distributed graph algorithms for computer network applications, with a particular emphasis on practical implementation. Topics and features: introduces a range of fundamental graph algorithms, covering spanning trees, graph traversal algorithms, routing algorithms, and self-stabilization; reviews graph-theoretical distributed approximation algorithms with applications in ad hoc wireless networks; describes in detail the implementation of each algorithm, with extensive use of supporting examples, and discusses their concrete network applications; examines key graph-theoretical algorithm concepts, such as dominating sets, and parameters for mobility and energy levels of nodes in wireless ad hoc networks, and provides a contemporary survey of each topic; presents a simple simulator, developed to run distributed algorithms; provides practical exercises at the end of each chapter.

Project Report from the year 2015 in the subject Computer Science - IT-Security, Central Queensland University (Theory Lab), language: English, abstract: Graph theory has become a very critical component in many applications in the computing field including networking and security. Unfortunately, it is also amongst the most complex topics to understand and apply. In this paper, we review some of the key applications of graph theory in network security. We first cover some algorithmic aspects, then present network coding and its relation to routing. The rapid growth in Global mobile communication networks demands new solutions for existing problems. Such problems include reduced bandwidth in mobile devices and the constant change in their associated network topologies. This creates a need for network algorithms with: 1. least possible communication traffic 2. High speed execution. The two challenges can be overcome by application of graph theory in developing local algorithms (Algorithms that require low rounds of communication). In this paper we explore applications of graph theory in cellular networks with an emphasis on the 'four-color' theorem and network coding and their relevant applications in wireless mobile networks.

This monograph treats the application of numerous graph-theoretic algorithms to a comprehensive analysis of dynamic enterprise networks. Network dynamics analysis yields valuable information about network performance, efficiency, fault prediction, cost optimization, indicators and warnings. Based on many years of applied research on generic network dynamics, this work covers a number of elegant applications (including many new and experimental results) of traditional graph theory algorithms and techniques to computationally tractable network dynamics analysis to motivate network analysts, practitioners and researchers alike.

The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path problem, and an exposition of a broad range of applications. First of all, the shortest path problem is presented so as to fix terminology and concepts: existence and uniqueness of solutions, robustness to parameter changes, and centralized and distributed computation algorithms. Then, these concepts are generalized to the algebraic context of semirings. Methods for creating new semirings, useful for modeling new problems, are provided. A large part of the book is then devoted to numerous applications of the algebraic path problem, ranging from mobile network routing to BGP routing to social networks. These applications show what kind of problems can be modeled as algebraic path problems; they also serve as examples on how to go about modeling new problems. This monograph will be useful to network researchers, engineers, and graduate students. It can be used either as an introduction to the topic, or as a quick reference to the theoretical facts, algorithms, and application examples. The theoretical background assumed for the reader is that of a graduate or advanced undergraduate student in computer science or engineering. Some familiarity with algebra and algorithms is helpful, but not necessary. Algebra, in particular, is used as a convenient and concise language to describe problems that are essentially combinatorial. Table of Contents: Classical Shortest Path / The Algebraic Path Problem / Properties and Computation of Solutions / Applications / Related Areas / List of Semirings and Applications

This brief focuses on introducing a novel mathematical framework, referred as hypergraph theory, to model and solve the multiple interferer scenarios for future wireless communication networks. First, in Chap. 1, the authors introduce the basic preliminaries of hypergraph theory in general, and develop two hypergraph based polynomial algorithms, i.e., hypergraph coloring and hypergraph clustering. Then, in Chaps. 2 and 3, the authors present two emerging applications of hypergraph coloring and hypergraph clustering in Device-to-Device (D2D) underlay communication networks, respectively, in order to show the advantages of hypergraph theory compared with the traditional graph theory. Finally, in Chap. 4, the authors discuss the limitations of using hypergraph theory in future wireless networks and briefly present some other potential applications. This brief introduces the state-of-the-art research on the hypergraph theory and its applications in wireless communications. An efficient framework is provided for the researchers, professionals and advanced level students who are interested in the radio resource allocation in the heterogeneous networks to solve the resource allocation and interference management problems.

This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.

This book gives a comprehensive presentation of cutting-edge research in communication networks with a combinatorial optimization component. The objective of the book is to advance and promote the theory and applications of combinatorial optimization in communication networks. Each chapter is written by an expert dealing with theoretical, computational, or applied aspects of combinatorial optimization.

Modeling networks as different graph types and discovering novel route finding strategies, as well as avoiding congestion in dense subnetworks via graph-theoretic approaches, contribute to overall blocking probability reduction in communication networks. We develop methods for modeling congested subnetworks and graph density measures to identify routes that avoid dense subgraphs for local or global congestion avoidance. We thoroughly review various concepts of graph density, as well as associated theorems and algorithms to identify and extract a densest subgraph from an input graph, according to different definitions of graph density. The Disjoint Connecting Paths problem, and its capacitated generalization, called Unsplittable Flow problem, play an important role in practical applications such as communication network design and routing. These tasks are NP-hard in general, but various polynomialtime approximations and efficiently solvable special cases are known. We present a solution that provides a relatively simple, efficient algorithm for the Unsplittable Flow problem in large, general directed graphs, where the task is NP-hard, and is known to remain NP-hard even to approximate up to a large factor. The efficiency of our algorithm is achieved by sacrificing a small part of the solution space. This also represents a novel paradigm for approximation: rather than giving up the search for an exact solution, we restrict the solution space to a subset that is the most important for applications, and excludes only a small part that is marginal in some well-defined sense. Specifically, the sacrificed part only contains scenarios where some edges are very close to saturation. Since nearly saturated links are undesirable in practical applications, therefore, excluding near-saturation is quite reasonable from the practical point of view. Referring the solutions that contain no nearly saturated edges as safe solutions, and call the approach safe approximation we prove that this safe approximation can be carried out efficiently. That is, once we restrict ourselves to safe solutions, but keeping the graph completely general, finding the exact optimum by a randomized polynomial time algorithm is feasible. As a further piece of graph theory based analysis, we study random graphs instances in which the edges are allowed to be dependent. The importance of random graphs in networking is provided by the fact that they are frequently used to model the network topology of radio networks. However, the most studied variant of random graph models, the Erd ̋os-Rényi random graph, is insufficient for this purpose, because of its strong simplifying assumption that the edges are stochastically independent. We generalize this model by allowing edge dependence, in a quite general way. We call our model p-robust random graph. It means that every edge is present at least with a given probability p, regardless of the presence/absence of other edges. This allows significant dependencies, but keeping independent edges as a special case. For our main result, we consider monotone graph properties: properties that are preserved whenever more edges are added. Many important graph properties are monotone. Our main result, which requires a rather sophisticated proof, is that for any monotone graph property, the p-robust random graph has at least as high probability to have the property as an Erd ̋os-Rényi random graph with edge probability p. This provides a useful general tool, as it allows the adaptation of many results from classical Erd ̋os-Rényi random graphs to a non-independent setting, via using them as lower bounds. Finally, to complement the theoretical investigations with a practical approach, we consider a fundamental component for packet traffic filtering in computer networks, called Access Control List (ACL). Packet filtering via ACL controls inbound or outbound packet traffic and provides the ability to manage the network traffic flow through a network element to optimize quality of service (QoS), network security, as well as network performance. In general, filtering packet traffic and applying rules of permit/denial to data packets flowing into network nodes are facilitated by ACL. As an industry use case, we propose a procedure of adding a link load threshold value to the Access Control List rules option, which acts on the basis of a threshold value. This enhanced ACL is helps to avoid congestion in targeted subnetworks via the link load threshold value, which allows to decide that the packet traffic is rerouted by the router to avoid congestion, or packet drop is initiated on the basis of packet priorities. We demonstrate the system operation via numerical simulation.