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Following the pattern of the Internet growth in popularity, started in the early 1990s, the current unprecedented expansion of wireless technology promises to have an even greater effect on how people communicate and interact, with considerable socio-economic impact all over the world. The driving force behind this growth is the remarkable progress in component miniaturization, integration, and also devel- ments in waveforms, coding, and communication protocols. Besides established infrastructurebased wireless networks (cellular, WLAN, sat- lite) ad-hoc wireless networks emerge as a new platform for distributed applications and for personal communication in scenarios where deploying infrastructure is not feasible. In ad-hoc wireless networks, each node is capable of forwarding packets on behalf of other nodes, so that multi-hop paths provide end-to-end connectivity. The increased flexibility and mobility of ad-hoc wireless networks are favored for appli- tions in law enforcement, homeland defense and military. In a world where wireless networks become increasingly interoperable with each other and with the high-speed wired Internet, personal communication systems will transform into universal terminals with instant access to variate content and able of handle demanding tasks, such as multimedia and real-time video. With users roaming between networks, and with wide variation in wireless link quality even in a single domain, the communications terminal must continue to provide a level of Quality of Service that is acceptable to the user and conforms to a contracted Service Level Agreement.

This book identifies vulnerabilities in the physical layer, the MAC layer, the IP layer, the transport layer, and the application layer, of wireless networks, and discusses ways to strengthen security mechanisms and services. Topics covered include intrusion detection, secure PHY/MAC/routing protocols, attacks and prevention, immunization, key management, secure group communications and multicast, secure location services, monitoring and surveillance, anonymity, privacy, trust establishment/management, redundancy and security, and dependable wireless networking.

Combinatorial optimization algorithms are used in many applications including the design, management, and operations of communication networks. The objective of this book is to advance and promote the theory and applications of combinatorial optimization in communication networks. Each chapter of the book is written by an expert dealing with theoretical, computational, or applied aspects of combinatorial optimization.Topics covered in the book include the combinatorial optimization problems arising in optical networks, wireless ad hoc networks, sensor networks, mobile communication systems, and satellite networks. A variety of problems are addressed using combinatorial optimization techniques, ranging from routing and resource allocation to QoS provisioning.

Over the past two decades, network technologies have been remarkably renovated and computer networks, particularly the Internet, have permeated into every facet of our daily lives. These changes also brought about new challenges, particularly in the area of security. Network security is essential to protect data integrity, con?d- tiality, access control, authentication, user privacy, and so on. All of these aspects are critical to provide fundamental network functionalities. This book covers a comprehensive array of topics in network security including secure metering, group key management, DDoS attacks, and many others. It can be used as a handy reference book for researchers, educators, graduate students, as well as professionals in the ?eld of network security. This book contains 11 r- ereed chapters from prominent researchers working in this area around the globe. Although these selected topics could not cover every aspect, they do represent the most fundamental and practical techniques. This book has been made possible by the great efforts and contributions of many people. First, we thank the authors of each chapter for contributing informative and insightful chapters. Then, we thank all reviewers for their invaluable comments and suggestions that improved the quality of this book. Finally, we thank the staff m- bers from Springer for publishing this work. Besides, we would like to dedicate this book to our families.

Automata and natural language theory are topics lying at the heart of computer science. Both are linked to computational complexity and together, these disciplines help define the parameters of what constitutes a computer, the structure of programs, which problems are solvable by computers, and a range of other crucial aspects of the practice of computer science. In this important volume, two respected authors/editors in the field offer accessible, practice-oriented coverage of these issues with an emphasis on refining core problem solving skills.

2. The Algorithm ...59 3. Convergence Analysis ..., ...60 4. Complexity Analysis ...63 5. Conclusions ...67 References ...67 A Simple Proof for a Result of Ollerenshaw on Steiner Trees ...68 Xiufeng Du, Ding-Zhu Du, Biao Gao, and Lixue Qii 1. Introduction ...68 2. In the Euclidean Plane ...69 3. In the Rectilinear Plane ...70 4. Discussion ...-...71 References ...71 Optimization Algorithms for the Satisfiability (SAT) Problem ...72 Jun Gu 1. Introduction ...72 2. A Classification of SAT Algorithms ...7:3 3. Preliminaries ...IV 4. Complete Algorithms and Incomplete Algorithms ...81 5. Optimization: An Iterative Refinement Process ...86 6. Local Search Algorithms for SAT ...89 7. Global Optimization Algorithms for SAT Problem ...106 8. Applications ...137 9. Future Work ...140 10. Conclusions ...141 References ...143 Ergodic Convergence in Proximal Point Algorithms with Bregman Functions ...155 Osman Guier 1. Introduction ...: ...155 2. Convergence for Function Minimization ...158 3. Convergence for Arbitrary Maximal Monotone Operators ...161 References ...163 Adding and Deleting Constraints in the Logarithmic Barrier Method for LP ...166 D. den Hertog, C. Roos, and T. Terlaky 1.Introduction ...16(5 2. The Logarithmic Darrier Method ...lG8 CONTENTS IX 3. The Effects of Shifting, Adding and Deleting Constraints ...171 4. The Build-Up and Down Algorithm ...177 ...5. Complexity Analysis ...180 References ...184 A Projection Method for Solving Infinite Systems of Linear Inequalities ...186 Hui Hu 1. Introduction ...186 2. The Projection Method ...186 3. Convergence Rate ...189 4. Infinite Systems of Convex Inequalities ...191 5. Application ...193 References ...

Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.

A basic problem for the interconnection of communications media is to design interconnection networks for specific needs. For example, to minimize delay and to maximize reliability, networks are required that have minimum diameter and maximum connectivity under certain conditions. This work provides a recent solution to this problem. The subject of all five chapters is the interconnection problem. The first two chapters deal with Cayley digraphs which are candidates for networks of maximum connectivity with given degree and number of nodes. Chapter 3 addresses Bruijn digraphs, Kautz digraphs and their generalizations, which are candidates for networks of minimum diameter and maximum connectivity with given degree and number of nodes. Chapter 4 studies double loop networks, and Chapter 5 considers broadcasting and the gossiping problem.

This book contains a collection of survey papers in the areas of algorithms, lan­ guages and complexity, the three areas in which Professor Ronald V. Book has made significant contributions. As a fonner student and a co-author who have been influenced by him directly, we would like to dedicate this book to Professor Ronald V. Book to honor and celebrate his sixtieth birthday. Professor Book initiated his brilliant academic career in 1958, graduating from Grinnell College with a Bachelor of Arts degree. He obtained a Master of Arts in Teaching degree in 1960 and a Master of Arts degree in 1964 both from Wesleyan University, and a Doctor of Philosophy degree from Harvard University in 1969, under the guidance of Professor Sheila A. Greibach. Professor Book's research in discrete mathematics and theoretical com­ puter science is reflected in more than 150 scientific publications. These works have made a strong impact on the development of several areas of theoretical computer science. A more detailed summary of his scientific research appears in this volume separately.

This three-volume set deals with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The editors have tried to bring together almost every aspect of the enormous field with emphasis on recent developments. Each chapter is essentially expository in nature, but of scholarly treatment. The work is addressed not only to researchers in discrete optimization, but to all scientists who use combinatorial optimization methods to model and solve problems. Experts in the field as well as nonspecialists should find the material helpful.

This volume can be considered as a supplementary volume to the three-volume "Handbook of Combinatorial Optimization" published by Kluwer. It can also be regarded as a stand-alone volume which presents chapters dealing with various aspects of the subject including optimization problems and algorithmic approaches for discrete problems. This handbook deals with several algorithmic approaches for discrete problems as well as with many combinatorial optimization problems. Each chapter in the handbook is expository in nature, but scholarly in treatment. The book is addressed not only to researchers in discrete optimization, but to all scientists in various disciplines who use combinatorial optimization methods to model and solve problems.

Presenting a set of contributions by the most influential authors on the Steiner Tree problem, the authors of this text address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications. The book is intended for advanced undergraduates, graduates and research scientists in combinational optimization and computer science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.

The switching net.work is an important. classic research area in t.ele- communication and comput.er net.works. It.s import.ancc st.ems from both theory and practice. In fact, some open problems, such as Benes conjec- ture on shuffle-exchange networks and Chung-Rmis conjecture on multi- rate rearrangeability, still attract many researchers and the further de- velopment in optical networks requires advanced technology in optical switching networks. In 1997, we had a workshop in switching networks held in NSF Sci- ence and Technology Center in Discrete Mathematics and Theoretical Computer Science (DIMACS), at Princeton University. This workshop was very successful. Many participants wished to have a similar activity every two or three years. This book is a result of such a wish. We are putting together SOllle important developments in this area during last. several years, including articles ill fault-tolerance, rearrang{~ability. non- blocking, optical networks. random permutation generat.ioll. and layout complexity. SOlllC of thos(~ art ides are research papers alld SOIllC an' sur- veys. All articles were reviewed.We would like to uWlItioll two special problems studied in those articles.

Optical networks with terabits per second bandwith have received significant interest from both researchers and practitioners. This book captures a collection of research and survey papers presenting developments in this area. Contributions are from active researchers and cover a wide range of topics, including static and dynamic wavelength assignment algorithms, optimized wavelength converter allocation, traffic scheduling for QoS support, connection management, multicast routing, terabit packet switch architectures, multifibre networks, and multistage interconnection networks. The articles summarize the existing techniques, current developments and future directions as well as propose novel solutions to some important problems.

The satisfiability (SAT) problem is central in mathematical logic, computing theory, and many industrial applications. There has been a strong relationship between the theory, the algorithms, and the applications of the SAT problem. This book aims to bring together work by the best theorists, algorithmists, and practitioners working on the SAT problem and on industrial applications, as well as to enhance the interaction between the three research groups. The book features the application of theoretical/algorithmic results to practical problems and presents practical problems for theoretical/algorithmic study.Major topics covered in the book include practical and industrial SAT problems and benchmarks, significant case studies and applications of the SAT problem and SAT algorithms, new algorithms and improved techniques for satisfiability testing, specific data structures and implementation details of the SAT algorithms, and the theoretical study of the SAT problem and SAT algorithms. It features: a comprehensive review of SAT research work over the past 25 years; the most recent research results; and a spectrum of algorithmic issues and applications.

Connectivity and facilities location are two important topics in network design, with applications in data communication, transportation, production planning, and VLSI designs. There are two issues concerning these topics: design and optimization. They involve combinatorial design and combinatorial optimization. This volume features talks presented at an interdisciplinary research workshop held at DIMACS in April 1997. The workshop was attended by leading theorists, algorithmists, and practitioners working on network design problems. Finding the solution of design problems and the optimal or approximate solution of the related optimization problem are challenging tasks because no polynomial time algorithms are known.Such problems include some variations of Steiner tree problems (such as multiple-connected Steiner network, independent flow problem, and subset-interconnection designs), topology network design, nonlinear assignment problems (such as quadratic assignment problems), problems in facilities location and allocation, and network problems appearing in VLSI design. The focus of this book is on combinatorial, algorithmic, and applicational aspects of these problems. The volume would be suitable as a textbook for advanced courses in computer science, mathematics, engineering, and operations research.

Praise for the First Edition"... complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity."—Zentralblatt MATHA thorough revision based on advances in the field of computational complexity and readers’ feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered.Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as: A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer scienceAdditional exercises at varying levels of difficulty to further test comprehension of the presented materialEnd-of-chapter literature reviews that summarize each topic and offer additional sources for further study Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.

Optimization is of central importance in all sciences. Nature inherently seeks optimal solutions. For example, light travels through the "shortest" path and the folded state of a protein corresponds to the structure with the "minimum" potential energy. In combinatorial optimization, there are numerous computationally hard problems arising in real world applications, such as floorplanning in VLSI designs and Steiner trees in communication networks. For these problems, the exact optimal solution is not currently real-time computable. One usually computes an approximate solution with various kinds of heuristics. Recently, many approaches have been developed that link the discrete space of combinatorial optimization to the continuous space of nonlinear optimization through geometric, analytic, and algebraic techniques. Many researchers have found that such approaches lead to very fast and efficient heuristics for solving large problems. Although almost all such heuristics work well in practice there is no solid theoretical analysis, except Karmakar's algorithm for linear programming. With this situation in mind, we decided to teach a seminar on nonlinear optimization with emphasis on its mathematical foundations. This book is the result of that seminar. During the last decades many textbooks and monographs in nonlinear optimization have been published. Why should we write this new one? What is the difference of this book from the others? The motivation for writing this book originated from our efforts to select a textbook for a graduate seminar with focus on the mathematical foundations of optimization.

The exponential scaling of feature sizes in semiconductor technologies has side-effects on layout optimization, related to effects such as interconnect delay, noise, crosstalk, signal integrity, parasitics effects and power dissipation, that invalidate the assumptions that form the basis of previous design methodologies and tools. This book is intended to sample the most important, contemporary and advanced layout optimization problems emerging with the advent of very deep submicron technologies in semiconductor processing. A reference work for graduate students, senior undergraduates and researchers.

This volume is a collection of 16 articles contributed by influential experts in the field of Steiner tree applications. The articles are designed to explore the impact on industries of the long-term theoretical development of Steiner tree problems. The authors address various Steiner tree problems originating from and applied to industry fields, such as the design of electronic circuits, telecommunication networks, computer networks, and computer biology. This book should be a good reference tool for scientists who depend on Steiner tree problems in some way.

Along with the explosive growth of network traffic, multiwavelength optical networks are believed to be the technology that will support the ever-increasing bandwidth demands and will be the backbone for the next generation of the Internet. This title systematically studies the major research issues in WDM (Wavelength Division Multiplexing) optical networks, such as routing and wavelength assignment, QoS multicast routing, design of logical topologies, and placement of wavelength converters. The book consists of two parts. The first part studies the fundamental concepts and principles of WDM networks. The second part discusses advanced and research issues of WDM networks.

Wireless networking enables two or more computers to communicate using standard network protocols without network cables. Since their emergence in the 1970s, wireless networks have become increasingly pop­ ular in the computing industry. In the past decade, wireless networks have enabled true mobility. There are currently two versions of mobile wireless networks. An infrastructure network contains a wired backbone with the last hop being wireless. The cellular phone system is an exam­ ple of an infrastructure network. A multihop ad hoc wireless network has no infrastructure and is thus entirely wireless. A wireless sensor network is an example of a multihop ad hoc wireless network. Ad hoc wireless networking is a technique to support robust and ef­ ficient operation in mobile wireless networks by incorporating routing functionality into mobile hosts. This technique will be used to realize the dream of "anywhere and anytime computing", which is termed mo­ bile computing. Mobile computing is a new paradigm of computing in which users carrying portable devices have access to shared infrastruc­ ture in any location at any time. Mobile computing is a very challenging topic for scientists in computer science and electrical engineering. The representative system for ad hoc wireless networking is called MANET, an acronym for "Mobile Ad hoc NETworks". MANET is an autonomous system consisting of mobile hosts connected by wireless links which can be quickly deployed.

This is the first book that provides readers with a deep technical overview of recent advances in resource management for wireless networks at different layers of the protocol stack. The subject is explored in various wireless networks, such as ad hoc wireless networks, 3G/4G cellular, IEEE 802.11, and Bluetooth personal area networks. Survey chapters give an excellent introduction to key topics in resource management for wireless networks, while experts will be satisfied by the technical depth of the knowledge imparted in chapters exploring hot research topics. The subject area discussed in this book is very relevant today, considering the recent remarkable growth of wireless networking and the convergence of wireless personal communications, internet technologies and real-time multimedia. This volume is a very good companion for practitioners working on implementing solutions for multimedia and Quality of Service -- sensitive applications over wireless networks.

This book identifies vulnerabilities in the physical layer, the MAC layer, the IP layer, the transport layer, and the application layer, of wireless networks, and discusses ways to strengthen security mechanisms and services. Topics covered include intrusion detection, secure PHY/MAC/routing protocols, attacks and prevention, immunization, key management, secure group communications and multicast, secure location services, monitoring and surveillance, anonymity, privacy, trust establishment/management, redundancy and security, and dependable wireless networking.

Combinatorial optimization algorithms are used in many applications including the design, management, and operations of communication networks. The objective of this book is to advance and promote the theory and applications of combinatorial optimization in communication networks. Each chapter of the book is written by an expert dealing with theoretical, computational, or applied aspects of combinatorial optimization.Topics covered in the book include the combinatorial optimization problems arising in optical networks, wireless ad hoc networks, sensor networks, mobile communication systems, and satellite networks. A variety of problems are addressed using combinatorial optimization techniques, ranging from routing and resource allocation to QoS provisioning.

A basic problem for the interconnection of communications media is to design interconnection networks for specific needs. For example, to minimize delay and to maximize reliability, networks are required that have minimum diameter and maximum connectivity under certain conditions. The book provides a recent solution to this problem. The subject of all five chapters is the interconnection problem. The first two chapters deal with Cayley digraphs which are candidates for networks of maximum connectivity with given degree and number of nodes. Chapter 3 addresses Bruijn digraphs, Kautz digraphs, and their generalizations, which are candidates for networks of minimum diameter and maximum connectivity with given degree and number of nodes. Chapter 4 studies double loop networks, and Chapter 5 considers broadcasting and the Gossiping problem. All the chapters emphasize the combinatorial aspects of network theory. Audience: A vital reference for graduate students and researchers in applied mathematics and theoretical computer science.

Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math­ ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air­ line crew scheduling, corporate planning, computer-aided design and man­ ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca­ tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover­ ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo­ rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi­ tion, linear programming relaxations are often the basis for many approxi­ mation algorithms for solving NP-hard problems (e.g. dualheuristics).

This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications. Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.

Optimization is of central importance in all sciences. Nature inherently seeks optimal solutions. For example, light travels through the "shortest" path and the folded state of a protein corresponds to the structure with the "minimum" potential energy. In combinatorial optimization, there are numerous computationally hard problems arising in real world applications, such as floorplanning in VLSI designs and Steiner trees in communication networks. For these problems, the exact optimal solution is not currently real-time computable. One usually computes an approximate solution with various kinds of heuristics. Recently, many approaches have been developed that link the discrete space of combinatorial optimization to the continuous space of nonlinear optimization through geometric, analytic, and algebraic techniques. Many researchers have found that such approaches lead to very fast and efficient heuristics for solving large problems. Although almost all such heuristics work well in practice there is no solid theoretical analysis, except Karmakar's algorithm for linear programming. With this situation in mind, we decided to teach a seminar on nonlinear optimization with emphasis on its mathematical foundations. This book is the result of that seminar. During the last decades many textbooks and monographs in nonlinear optimization have been published. Why should we write this new one? What is the difference of this book from the others? The motivation for writing this book originated from our efforts to select a textbook for a graduate seminar with focus on the mathematical foundations of optimization.