Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties is a comprehensive book that explores the complexity of optimization problems and the design of approximation algorithms. The book is written by Giorgio Ausiello, Alberto Marchetti-Spaccamela, Giorgio Gambosi, Marco Protasi, and Viggo Kann. It is divided into ten chapters, each covering different aspects of approximation algorithms and their theoretical foundations. The first chapter introduces the complexity of optimization problems, including the concepts of NP-hardness and the classification of optimization problems into PO and NPO. The second chapter discusses various design techniques for approximation algorithms, such as the greedy method, local search, and dynamic programming. The third chapter focuses on approximation classes, including the classes APX, PTAS, and FPTAS, and their relationships. The fourth chapter explores input-dependent and asymptotic approximation, while the fifth chapter discusses approximation through randomization. The sixth chapter covers NP, PCP, and non-approximability results, including the PCP theorem. The seventh chapter provides a detailed explanation of the PCP theorem. The eighth chapter discusses approximation preserving reductions and their implications for the study of approximability. The ninth chapter presents probabilistic analysis of approximation algorithms, and the tenth chapter covers heuristic methods for solving optimization problems. The book also includes a comprehensive compendium of more than 200 optimization problems, along with their approximability properties. The book is intended for researchers and students in computer science and mathematics, and it provides a thorough understanding of the complexity of optimization problems and the design of approximation algorithms. The book is supported by an extensive bibliography and is accompanied by a detailed appendix that covers basic mathematical concepts and linear programming. The book is organized into four main reading threads, each focusing on different aspects of approximation algorithms and their theoretical foundations. The first thread covers the design and performance analysis of basic approximation algorithms, while the second thread explores advanced techniques for the design and analysis of approximation algorithms. The third thread focuses on the theoretical study of basic notions of approximation complexity, and the fourth thread is devoted to advanced concepts of approximation complexity and inapproximability results. The book is a valuable resource for anyone interested in the theory and practice of approximation algorithms.Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties is a comprehensive book that explores the complexity of optimization problems and the design of approximation algorithms. The book is written by Giorgio Ausiello, Alberto Marchetti-Spaccamela, Giorgio Gambosi, Marco Protasi, and Viggo Kann. It is divided into ten chapters, each covering different aspects of approximation algorithms and their theoretical foundations. The first chapter introduces the complexity of optimization problems, including the concepts of NP-hardness and the classification of optimization problems into PO and NPO. The second chapter discusses various design techniques for approximation algorithms, such as the greedy method, local search, and dynamic programming. The third chapter focuses on approximation classes, including the classes APX, PTAS, and FPTAS, and their relationships. The fourth chapter explores input-dependent and asymptotic approximation, while the fifth chapter discusses approximation through randomization. The sixth chapter covers NP, PCP, and non-approximability results, including the PCP theorem. The seventh chapter provides a detailed explanation of the PCP theorem. The eighth chapter discusses approximation preserving reductions and their implications for the study of approximability. The ninth chapter presents probabilistic analysis of approximation algorithms, and the tenth chapter covers heuristic methods for solving optimization problems. The book also includes a comprehensive compendium of more than 200 optimization problems, along with their approximability properties. The book is intended for researchers and students in computer science and mathematics, and it provides a thorough understanding of the complexity of optimization problems and the design of approximation algorithms. The book is supported by an extensive bibliography and is accompanied by a detailed appendix that covers basic mathematical concepts and linear programming. The book is organized into four main reading threads, each focusing on different aspects of approximation algorithms and their theoretical foundations. The first thread covers the design and performance analysis of basic approximation algorithms, while the second thread explores advanced techniques for the design and analysis of approximation algorithms. The third thread focuses on the theoretical study of basic notions of approximation complexity, and the fourth thread is devoted to advanced concepts of approximation complexity and inapproximability results. The book is a valuable resource for anyone interested in the theory and practice of approximation algorithms.