The computer science problem whose solution could transform life as we know it The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

This book provides a comprehensive analysis of the most important topics in parallel computation. It is written so that it may be used as a self-study guide to the field, and researchers in parallel computing will find it a useful reference for many years to come. The first half of the book consists of an introduction to many fundamental issues in parallel computing. The second half provides lists of P-complete- and open problems. These lists will have lasting value to researchers in both industry and academia. The lists of problems, with their corresponding remarks, the thorough index, and the hundreds of references add to the exceptional value of this resource. While the exciting field of parallel computation continues to expand rapidly, this book serves as a guide to research done through 1994 and also describes the fundamental concepts that new workers will need to know in coming years. It is intended for anyone interested in parallel computing, including senior level undergraduate students, graduate students, faculty, and people in industry. As an essential reference, the book will be needed in all academic libraries.

The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

"My absolute favorite for this kind of interview preparation is Steven Skiena’s The Algorithm Design Manual. More than any other book it helped me understand just how astonishingly commonplace ... graph problems are -- they should be part of every working programmer’s toolkit. The book also covers basic data structures and sorting algorithms, which is a nice bonus. ... every 1 – pager has a simple picture, making it easy to remember. This is a great way to learn how to identify hundreds of problem types." (Steve Yegge, Get that Job at Google) "Steven Skiena’s Algorithm Design Manual retains its title as the best and most comprehensive practical algorithm guide to help identify and solve problems. ... Every programmer should read this book, and anyone working in the field should keep it close to hand. ... This is the best investment ... a programmer or aspiring programmer can make." (Harold Thimbleby, Times Higher Education) "It is wonderful to open to a random spot and discover an interesting algorithm. This is the only textbook I felt compelled to bring with me out of my student days.... The color really adds a lot of energy to the new edition of the book!" (Cory Bart, University of Delaware) "The is the most approachable book on algorithms I have." (Megan Squire, Elon University) --- This newly expanded and updated third edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficiency. It serves as the primary textbook of choice for algorithm design courses and interview self-study, 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, Practical Algorithm Design, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, the Hitchhiker's Guide to Algorithms, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations, and an extensive bibliography. NEW to the third edition: -- New and expanded coverage of randomized algorithms, hashing, divide and conquer, approximation algorithms, and quantum computing -- Provides full online support for lecturers, including an improved website component with lecture slides and videos -- Full color illustrations and code instantly clarify difficult concepts -- Includes several new "war stories" relating experiences from real-world applications -- Over 100 new problems, including programming-challenge problems from LeetCode and Hackerrank. -- Provides up-to-date links leading to the best implementations available in C, C++, and Java Additional Learning Tools: -- 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 -- Exercises include "job interview problems" from major software companies -- Highlighted "take home lessons" emphasize essential concepts -- The "no theorem-proof" style provides a uniquely accessible and intuitive approach to a challenging subject -- Many algorithms are presented with actual code (written in C) -- Provides comprehensive references to both survey articles and the primary literature Written by a well-known algorithms researcher who received the IEEE Computer Science and Engineering Teaching Award, this substantially enhanced third edition of The Algorithm Design Manual is an essential learning tool for students and professionals needed a solid grounding in algorithms. Professor Skiena is also the author of the popular Springer texts, The Data Science Design Manual and Programming Challenges: The Programming Contest Training Manual.

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.

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include:The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text DasGupta also offers a Solutions Manual which is available on the Online Learning Center."Algorithms is an outstanding undergraduate text equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel it is a joy to read." Tim Roughgarden Stanford University

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.