The intended readership includes both undergraduate and graduate students majoring in computer science as well as researchers in the computer science area. The book is suitable either as a textbook or as a supplementary book in algorithm courses. Over 400 computational problems are covered with various algorithms to tackle them. Rather than providing students simply with the best known algorithm for a problem, this book presents various algorithms for readers to master various algorithm design paradigms. Beginners in computer science can train their algorithm design skills via trivial algorithms on elementary problem examples. Graduate students can test their abilities to apply the algorithm design paradigms to devise an efficient algorithm for intermediate-level or challenging problems. Key Features: Dictionary of computational problems: A table of over 400 computational problems with more than 1500 algorithms is provided. Indices and Hyperlinks: Algorithms, computational problems, equations, figures, lemmas, properties, tables, and theorems are indexed with unique identification numbers and page numbers in the printed book and hyperlinked in the e-book version. Extensive Figures: Over 435 figures illustrate the algorithms and describe computational problems. Comprehensive exercises: More than 352 exercises help students to improve their algorithm design and analysis skills. The answers for most questions are available in the accompanying solution manual.

This solution manual is to accompany the book entitled “7 Algorithm Design Paradigms.” It is strongly recommended that students attempt the exercises without this solution manual, in order to improve their knowledge and skills.

Presenting a complementary perspective to standard books on algorithms, A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis provides a roadmap for readers to determine the difficulty of an algorithmic problem by finding an optimal solution or proving complexity results. It gives a practical treatment of algorithmic complexity and guides readers in solving algorithmic problems. Divided into three parts, the book offers a comprehensive set of problems with solutions as well as in-depth case studies that demonstrate how to assess the complexity of a new problem. Part I helps readers understand the main design principles and design efficient algorithms. Part II covers polynomial reductions from NP-complete problems and approaches that go beyond NP-completeness. Part III supplies readers with tools and techniques to evaluate problem complexity, including how to determine which instances are polynomial and which are NP-hard. Drawing on the authors’ classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity. Through many problems and detailed examples, readers can investigate polynomial-time algorithms and NP-completeness and beyond.

Presenting a complementary perspective to standard books on algorithms, A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis provides a roadmap for readers to determine the difficulty of an algorithmic problem by finding an optimal solution or proving complexity results. It gives a practical treatment of algorithmic complexity and guides readers in solving algorithmic problems. Divided into three parts, the book offers a comprehensive set of problems with solutions as well as in-depth case studies that demonstrate how to assess the complexity of a new problem. Part I helps readers understand the main design principles and design efficient algorithms. Part II covers polynomial reductions from NP-complete problems and approaches that go beyond NP-completeness. Part III supplies readers with tools and techniques to evaluate problem complexity, including how to determine which instances are polynomial and which are NP-hard. Drawing on the authors’ classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity. Through many problems and detailed examples, readers can investigate polynomial-time algorithms and NP-completeness and beyond.

Systematically teaches key paradigmic algorithm design methods Provides a deep insight into randomization

Algorithms Illuminated is an accessible introduction to algorithms for anyone with at least a little programming experience, based on a sequence of popular online courses. Part 1 covers asymptotic analysis and big-O notation, divide-and-conquer algorithms, randomized algorithms, and several famous algorithms for sorting and selection.

This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: • Doubles the tutorial material and exercises over the first edition • Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video • Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them • Includes several NEW "war stories" relating experiences from real-world applications • Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java

Formal Design Theory (PDT) is a mathematical theory of design. The main goal of PDT is to develop a domain independent core model of the design process. The book focuses the reader's attention on the process by which ideas originate and are developed into workable products. In developing PDT, we have been striving toward what has been expressed by the distinguished scholar Simon (1969): that "the science of design is possible and some day we will be able to talk in terms of well-established theories and practices. " The book is divided into five interrelated parts. The conceptual approach is presented first (Part I); followed by the theoretical foundations of PDT (Part II), and from which the algorithmic and pragmatic implications are deduced (Part III). Finally, detailed case-studies illustrate the theory and the methods of the design process (Part IV), and additional practical considerations are evaluated (Part V). The generic nature of the concepts, theory and methods are validated by examples from a variety of disciplines. FDT explores issues such as: algebraic representation of design artifacts, idealized design process cycle, and computational analysis and measurement of design process complexity and quality. FDT's axioms convey the assumptions of the theory about the nature of artifacts, and potential modifications of the artifacts in achieving desired goals or functionality. By being able to state these axioms explicitly, it is possible to derive theorems and corollaries, as well as to develop specific analytical and constructive methodologies.

Get started with C++ programming by learning how to build applications using its data structures and algorithms Key FeaturesExplore data structures such as arrays, stacks, and graphs with real-world examplesStudy the trade-offs between algorithms and data structures and discover what works and what doesn'tDiscover how techniques such as bloom filters and multi-way heaps boost real-world applicationsBook Description C++ is a mature multi-paradigm programming language that enables you to write high-level code with a high degree of control over the hardware. Today, significant parts of software infrastructure, including databases, browsers, multimedia frameworks, and GUI toolkits, are written in C++. This book starts by introducing C++ data structures and how to store data using linked lists, arrays, stacks, and queues. In later chapters, the book explains the basic algorithm design paradigms, such as the greedy approach and the divide-and-conquer approach, which are used to solve a large variety of computational problems. Finally, you will learn the advanced technique of dynamic programming to develop optimized implementations of several algorithms discussed in the book. By the end of this book, you will have learned how to implement standard data structures and algorithms in efficient and scalable C++ 14 code. What you will learnBuild applications using hash tables, dictionaries, and setsExplore how modern hardware affects the actual run-time performance of programsApply common algorithms such as heapsort and merge sort for string data typesUse C++ template metaprogramming to write code librariesImplement a URL shortening service using a bloom filterUse appropriate modern C++ idioms such as std:: array instead of C-style arraysWho this book is for This book is for developers or students who want to revisit basic data structures and algorithm design techniques. Although no mathematical background is required, basic knowledge of complexity classes and Big O notation along with a qualification in an algorithms course will help you get the most out of this book. Familiarity with C++ 14 standard is assumed.

This dissertation formalizes the intuitive notion of the basic algorithmic paradigms. We present three formal models which aim to capture the intrinsic power of greedy, backtracking and dynamic programming algorithms. We develop lower bound techniques for proving negative results for all algorithms in all models, which allow us to make strong statements about the limitations of each paradigm. Borodin et al. (2003) designed the Priority algorithms, a formal model of greedy algorithms for scheduling problems. We generalized the priority model to arbitrary problem domain and in particular graph problems and develop a lower bound technique for proving negative results for the class of all priority algorithms. We use the lower bound technique to show that finding shortest path in graphs with negative weights cannot be solved by a priority algorithm. We also prove that Dijkstra's algorithm is inherently adaptive and cannot be made non-adaptive. We show inapproximability results within the model for minimum weighted vertex cover, minimum metric Steiner tree, and maximum independent set problems. We develop a new 1.8-approximation scheme for the Steiner(1,2) problem. Alekhnovich et al. (2005) presented a model of backtracking and dynamic programming algorithms called prioritized Branching Trees (pBT). We generalize their model to allow free branching and call this new model prioritized Free Branching Tree (pFBT) algorithms and developed a lower bound technique for proving negative results for randomized priority algorithms, pBT and pFBT algorithms. We use the technique to prove that pBT algorithms require exponential width to solve the 7-SAT problem and that pFBT algorithms require width of 2^(\sqrt {n})} to solve the 7-SAT problem. Bellman-Ford is a classical dynamic programming algorithm and we show that pBT algorithms require width of 2^{\Omega(n^{1/9})} to solve the shortest path problem in graphs with negative weights exactly. Next we develop a stronger model of dynamic programming algorithms called prioritized Branching Programs (pBP). pBP algorithms can simulate pBT algorithms at no additional cost but also capture the notion of memoization which we believe is an essential part of the dynamic programming paradigm. We show that this class of algorithms can solve the shortest paths in graphs with negative weights but no negative cycles efficiently. We also show that two pBP sub-models can be simulated by pBT algorithms.