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| example of np hard problem: The Golden Ticket Lance Fortnow, 2017-02-28 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. |
| example of np hard problem: P, NP, and NP-Completeness Oded Goldreich, 2010-08-16 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. |
| example of np hard problem: Algorithms Sanjoy Dasgupta, Christos H. Papadimitriou, Umesh Virkumar Vazirani, 2006 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 |
| example of np hard problem: Introduction To Algorithms Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, Clifford Stein, 2001 An extensively revised edition of a mathematically rigorous yet accessible introduction to algorithms. |
| example of np hard problem: Computational Complexity Sanjeev Arora, Boaz Barak, 2009-04-20 New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students. |
| example of np hard problem: Approximation Algorithms for NP-hard Problems Dorit S. Hochbaum, 1997 This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms. Among the techniques discussed: the use of linear programming, primal-dual techniques in worst-case analysis, semidefinite programming, computational geometry techniques, randomized algorithms, average-case analysis, probabilistically checkable proofs and inapproximability, and the Markov Chain Monte Carlo method. The text includes a variety of pedagogical features: definitions, exercises, open problems, glossary of problems, index, and notes on how best to use the book. |
| example of np hard problem: Complexity and Real Computation Lenore Blum, Felipe Cucker, Michael Shub, Steve Smale, 2012-12-06 The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. |
| example of np hard problem: In Pursuit of the Traveling Salesman William J. Cook, 2014-11-09 The story of one of the greatest unsolved problems in mathematics What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics—and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today’s state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem. |
| example of np hard problem: Parameterized Algorithms Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh, 2015-07-20 This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work. |
| example of np hard problem: The Outer Limits of Reason Noson S. Yanofsky, 2016-11-04 This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. |
| example of np hard problem: Algorithmics for Hard Problems Juraj Hromkovič, 2014-03-12 An introduction to the methods of designing algorithms for hard computing tasks, concentrating mainly on approximate, randomized, and heuristic algorithms, and on the theoretical and experimental comparison of these approaches according to the requirements of the practice. This is the first book to systematically explain and compare all the main possibilities of attacking hard computing problems. It also closes the gap between theory and practice by providing at once a graduate textbook and a handbook for practitioners dealing with hard computing problems. |
| example of np hard problem: Nonnegative Matrix Factorization Nicolas Gillis, 2020-12-18 Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization. |
| example of np hard problem: Limits to Parallel Computation Raymond Greenlaw, H. James Hoover, Walter L. Ruzzo, 1995 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. |
| example of np hard problem: Grit Angela Duckworth, 2016-05-03 In this instant New York Times bestseller, Angela Duckworth shows anyone striving to succeed that the secret to outstanding achievement is not talent, but a special blend of passion and persistence she calls “grit.” “Inspiration for non-geniuses everywhere” (People). The daughter of a scientist who frequently noted her lack of “genius,” Angela Duckworth is now a celebrated researcher and professor. It was her early eye-opening stints in teaching, business consulting, and neuroscience that led to her hypothesis about what really drives success: not genius, but a unique combination of passion and long-term perseverance. In Grit, she takes us into the field to visit cadets struggling through their first days at West Point, teachers working in some of the toughest schools, and young finalists in the National Spelling Bee. She also mines fascinating insights from history and shows what can be gleaned from modern experiments in peak performance. Finally, she shares what she’s learned from interviewing dozens of high achievers—from JP Morgan CEO Jamie Dimon to New Yorker cartoon editor Bob Mankoff to Seattle Seahawks Coach Pete Carroll. “Duckworth’s ideas about the cultivation of tenacity have clearly changed some lives for the better” (The New York Times Book Review). Among Grit’s most valuable insights: any effort you make ultimately counts twice toward your goal; grit can be learned, regardless of IQ or circumstances; when it comes to child-rearing, neither a warm embrace nor high standards will work by themselves; how to trigger lifelong interest; the magic of the Hard Thing Rule; and so much more. Winningly personal, insightful, and even life-changing, Grit is a book about what goes through your head when you fall down, and how that—not talent or luck—makes all the difference. This is “a fascinating tour of the psychological research on success” (The Wall Street Journal). |
| example of np hard problem: Approximation Algorithms Vijay V. Vazirani, 2013-03-14 Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians. |
| example of np hard problem: Introduction to the Theory of Complexity Daniel Pierre Bovet, Pierluigi Crescenzi, 1994 Using a balanced approach that is partly algorithmic and partly structuralist, this book systematically reviews the most significant results obtained in the study of computational complexity theory. Features over 120 worked examples, over 200 problems, and 400 figures. |
| example of np hard problem: What Can Be Computed? John MacCormick, 2018-05-01 An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com |
| example of np hard problem: Computational Complexity and Feasibility of Data Processing and Interval Computations V. Kreinovich, A.V. Lakeyev, J. Rohn, P.T. Kahl, 2013-06-29 Targeted audience • Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. • Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. • Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing. |
| example of np hard problem: Dynamic Programming Art Lew, Holger Mauch, 2006-10-09 This book provides a practical introduction to computationally solving discrete optimization problems using dynamic programming. From the examples presented, readers should more easily be able to formulate dynamic programming solutions to their own problems of interest. We also provide and describe the design, implementation, and use of a software tool that has been used to numerically solve all of the problems presented earlier in the book. |
| example of np hard problem: Algorithms Illuminated, Part 1 Tim Roughgarden, 2017-09-27 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. |
| example of np hard problem: Protein Physics Alexei V. Finkelstein, Oleg Ptitsyn, 2016-06-22 Protein Physics: A Course of Lectures covers the most general problems of protein structure, folding and function. It describes key experimental facts and introduces concepts and theories, dealing with fibrous, membrane, and water-soluble globular proteins, in both their native and denatured states. The book systematically summarizes and presents the results of several decades of worldwide fundamental research on protein physics, structure, and folding, describing many physical models that help readers make estimates and predictions of physical processes that occur in proteins. New to this revised edition is the inclusion of novel information on amyloid aggregation, natively disordered proteins, protein folding in vivo, protein motors, misfolding, chameleon proteins, advances in protein engineering & design, and advances in the modeling of protein folding. Further, the book provides problems with solutions, many new and updated references, and physical and mathematical appendices. In addition, new figures (including stereo drawings, with a special appendix showing how to use them) are added, making this an ideal resource for graduate and advanced undergraduate students and researchers in academia in the fields of biophysics, physics, biochemistry, biologists, biotechnology, and chemistry. - Fully revised and expanded new edition based on the latest research developments in protein physics - Written by the world's top expert in the field - Deals with fibrous, membrane, and water-soluble globular proteins, in both their native and denatured states - Summarizes, in a systematic form, the results of several decades of worldwide fundamental research on protein physics and their structure and folding - Examines experimental data on protein structure in the post-genome era |
| example of np hard problem: No Country for Old Men Cormac McCarthy, 2007-11-29 From the bestselling author of The Passenger and the Pulitzer Prize–winning novel The Road comes a profoundly disturbing and gorgeously rendered novel (The Washington Post) that returns to the Texas-Mexico border, setting of the famed Border Trilogy. The time is our own, when rustlers have given way to drug-runners and small towns have become free-fire zones. One day, a good old boy named Llewellyn Moss finds a pickup truck surrounded by a bodyguard of dead men. A load of heroin and two million dollars in cash are still in the back. When Moss takes the money, he sets off a chain reaction of catastrophic violence that not even the law—in the person of aging, disillusioned Sheriff Bell—can contain. As Moss tries to evade his pursuers—in particular a mysterious mastermind who flips coins for human lives—McCarthy simultaneously strips down the American crime novel and broadens its concerns to encompass themes as ancient as the Bible and as bloodily contemporary as this morning’s headlines. No Country for Old Men is a triumph. Look for Cormac McCarthy's latest bestselling novels, The Passenger and Stella Maris. |
| example of np hard problem: Java Programming Ralph Bravaco, Shai Simonson, 2009-02-01 Java Programming, From The Ground Up, with its flexible organization, teaches Java in a way that is refreshing, fun, interesting and still has all the appropriate programming pieces for students to learn. The motivation behind this writing is to bring a logical, readable, entertaining approach to keep your students involved. Each chapter has a Bigger Picture section at the end of the chapter to provide a variety of interesting related topics in computer science. The writing style is conversational and not overly technical so it addresses programming concepts appropriately. Because of the flexibile organization of the text, it can be used for a one or two semester introductory Java programming class, as well as using Java as a second language. The text contains a large variety of carefully designed exercises that are more effective than the competition. |
| example of np hard problem: Recent Findings in Intelligent Computing Techniques Pankaj Kumar Sa, Sambit Bakshi, Ioannis K. Hatzilygeroudis, Manmath Narayan Sahoo, 2018-11-05 This three volume book contains the Proceedings of 5th International Conference on Advanced Computing, Networking and Informatics (ICACNI 2017). The book focuses on the recent advancement of the broad areas of advanced computing, networking and informatics. It also includes novel approaches devised by researchers from across the globe. This book brings together academic scientists, professors, research scholars and students to share and disseminate information on knowledge and scientific research works related to computing, networking, and informatics to discuss the practical challenges encountered and the solutions adopted. The book also promotes translation of basic research into applied investigation and convert applied investigation into practice. |
| example of np hard problem: The Traveling Salesman Problem D.B. Shmoys, J.K. Lenstra, A.H.G. Rinnooy Kan, E.L. Lawler, 1985 The Traveling Salesman Problem is central to the area of Combinatorial Optimization, and it is through this problem that many of the most important developments in the area have been made. This book focuses on essential ideas; through them it illustrates all the concepts and techniques of combinatorial optimization concisely but comprehensively. The extensive reference list and numerous exercises direct the reader towards related fields, and give results. Each of the twelve chapters in this volume is concerned with a specific aspect of the Traveling Salesman Problem, and is written by an authority on that aspect. It is hoped, that the book will serve as a state-of-the-art survey of the Traveling Salesman problem which will encourage further investigations, and that it will also be useful for its comprehensive coverage of the techniques of combinatorial optimization. |
| example of np hard problem: Stochastic Local Search Holger H. Hoos, Thomas Stützle, 2005 Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application. |
| example of np hard problem: Artificial Intelligence Stuart Russell, Peter Norvig, 2016-09-10 Artificial Intelligence: A Modern Approach offers the most comprehensive, up-to-date introduction to the theory and practice of artificial intelligence. Number one in its field, this textbook is ideal for one or two-semester, undergraduate or graduate-level courses in Artificial Intelligence. |
| example of np hard problem: The Nature of Computation Cristopher Moore, Stephan Mertens, 2011-08-11 Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again. |
| example of np hard problem: Beyond the Worst-Case Analysis of Algorithms Tim Roughgarden, 2021-01-14 Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks. |
| example of np hard problem: Complexity Theory Ingo Wegener, 2005-04-11 Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models All topics are considered from an algorithmic point of view stressing the implications for algorithm design |
| example of np hard problem: Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control Marko M Makela, Pekka Neittaanmaki, 1992-05-07 This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered. |
| example of np hard problem: Letter from Birmingham Jail Martin Luther King, 2025-01-14 A beautiful commemorative edition of Dr. Martin Luther King's essay Letter from Birmingham Jail, part of Dr. King's archives published exclusively by HarperCollins. With an afterword by Reginald Dwayne Betts On April 16, 1923, Dr. Martin Luther King Jr., responded to an open letter written and published by eight white clergyman admonishing the civil rights demonstrations happening in Birmingham, Alabama. Dr. King drafted his seminal response on scraps of paper smuggled into jail. King criticizes his detractors for caring more about order than justice, defends nonviolent protests, and argues for the moral responsibility to obey just laws while disobeying unjust ones. Letter from Birmingham Jail proclaims a message - confronting any injustice is an acceptable and righteous reason for civil disobedience. This beautifully designed edition presents Dr. King's speech in its entirety, paying tribute to this extraordinary leader and his immeasurable contribution, and inspiring a new generation of activists dedicated to carrying on the fight for justice and equality. |
| example of np hard problem: Sams Teach Yourself UML in 24 Hours Joseph Schmuller, 2004 Learn UML, the Unified Modeling Language, to create diagrams describing the various aspects and uses of your application before you start coding, to ensure that you have everything covered. Millions of programmers in all languages have found UML to be an invaluable asset to their craft. More than 50,000 previous readers have learned UML with Sams Teach Yourself UML in 24 Hours. Expert author Joe Schmuller takes you through 24 step-by-step lessons designed to ensure your understanding of UML diagrams and syntax. This updated edition includes the new features of UML 2.0 designed to make UML an even better modeling tool for modern object-oriented and component-based programming. The CD-ROM includes an electronic version of the book, and Poseidon for UML, Community Edition 2.2, a popular UML modeling tool you can use with the lessons in this book to create UML diagrams immediately. |
| example of np hard problem: An Efficient Parallel Biconnectivity Algorithm Robert E. Tarjan, U. Vishkin, 2018-02-07 This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| example of np hard problem: Evolutionary Multi-Criterion Optimization Heike Trautmann, Günter Rudolph, Kathrin Klamroth, Oliver Schütze, Margaret Wiecek, Yaochu Jin, Christian Grimme, 2017-02-17 This book constitutes the refereed proceedings of the 9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017 held in Münster, Germany in March 2017. The 33 revised full papers presented together with 13 poster presentations were carefully reviewed and selected from 72 submissions. The EMO 2017 aims to discuss all aspects of EMO development and deployment, including theoretical foundations; constraint handling techniques; preference handling techniques; handling of continuous, combinatorial or mixed-integer problems; local search techniques; hybrid approaches; stopping criteria; parallel EMO models; performance evaluation; test functions and benchmark problems; algorithm selection approaches; many-objective optimization; large scale optimization; real-world applications; EMO algorithm implementations. |
| example of np hard problem: Quantum Computing Since Democritus Scott Aaronson, 2013-03-14 Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics. |
| example of np hard problem: Complexity and Cryptography John Talbot, D. J. A. Welsh, 2006-01-12 Introductory textbook on Cryptography. |
| example of np hard problem: Learn Programming Antti Salonen, 2018-08-17 This book is aimed at readers who are interested in software development but have very little to no prior experience. The book focuses on teaching the core principles around software development. It uses several technologies to this goal (e.g. C, Python, JavaScript, HTML, etc.) but is not a book about the technologies themselves. The reader will learn the basics (or in some cases more) of various technologies along the way, but the focus is on building a foundation for software development. The book is your guided tour through the programming jungle, aiming to provide some clarity and build the foundation for software development skills. The book web site is https: //progbook.org/ |
| example of np hard problem: A First Course in Graph Theory Gary Chartrand, Ping Zhang, 2013-05-20 Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition. |
| example of np hard problem: Spectra of Graphs Andries E. Brouwer, Willem H. Haemers, 2011-12-17 This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included. |
EXAMPLE Definition & Meaning - Merriam-Webster
The meaning of EXAMPLE is one that serves as a pattern to be imitated or not to be imitated. How to use example in a sentence. Synonym Discussion of Example.
EXAMPLE | English meaning - Cambridge Dictionary
EXAMPLE definition: 1. something that is typical of the group of things that it is a member of: 2. a way of helping…. Learn more.
EXAMPLE Definition & Meaning | Dictionary.com
one of a number of things, or a part of something, taken to show the character of the whole. This painting is an example of his early work. a pattern or model, as of something to be imitated or …
Example - definition of example by The Free Dictionary
1. one of a number of things, or a part of something, taken to show the character of the whole. 2. a pattern or model, as of something to be imitated or avoided: to set a good example. 3. an …
Example Definition & Meaning - YourDictionary
To be illustrated or exemplified (by). Wear something simple; for example, a skirt and blouse.
EXAMPLE - Meaning & Translations | Collins English Dictionary
An example of something is a particular situation, object, or person which shows that what is being claimed is true. 2. An example of a particular class of objects or styles is something that …
example noun - Definition, pictures, pronunciation and usage …
used to emphasize something that explains or supports what you are saying; used to give an example of what you are saying. There is a similar word in many languages, for example in …
Example - Definition, Meaning & Synonyms - Vocabulary.com
An example is a particular instance of something that is representative of a group, or an illustration of something that's been generally described. Example comes from the Latin word …
example - definition and meaning - Wordnik
noun Something that serves as a pattern of behaviour to be imitated (a good example) or not to be imitated (a bad example). noun A person punished as a warning to others. noun A parallel …
EXAMPLE Synonyms: 20 Similar Words - Merriam-Webster
Some common synonyms of example are case, illustration, instance, sample, and specimen. While all these words mean "something that exhibits distinguishing characteristics in its …
11/1/2016 Nondeterministic Polynomial Time
NP‐complete and NP‐hard • Any NP problem can be reduced in polynomial time to an NP‐completeproblem Example: satisfiability • If any NP‐completeproblem can be solved in …
The Maximum Flow Problem - ripublication.com
It is an NP-hard problem and also one of the most well-known optimization problems in networks (network analysis is crucial in numerous fields such as geographical information systems …
P, NP and NP-Complete - GitHub Pages
NP-Hard and NP-Complete • If R is polynomial-time reducible to Q, we denote this R ≤ p Q • Definition of NP-Hard and NP-Complete: • If all problems R ∈ NP are polynomial-time …
1 Maximum Independent Set Problem
The MIS problem is the following: given a graph G= (V;E) nd an independent set in G of maximum cardinality. In the weighted case, each node v2V has an associated non-negative weight w(v) …
CS 583: Approximation Algorithms: Covering Problems
Set Cover problem is the Maximum Coverage problem. In this problem the input is again U and Sbut we are also given an integer k m. The goal is to select ksubsets from Ssuch that their …
Tree Decompositions, Treewidth, and NP-Hard Problems
short example is provided for which, in general, no deterministic polynomial time algorithm is known, but which turns out to be e ciently solvable for bounded ... Although the maximum …
P NP- - New York University
Another class of optimisation problems is known as NP-hard problems. For such problems, no polynomial-time algorithms are known and it is generally believed that these problems cannot …
MixedIntegerLinearProgramming - Computer Science …
Complexity: LPvs. IP 3/61 Including integer variables increases enourmously the modeling power, at the expense of more complexity LP’s can be solved in polynomial time with interior-point …
Chapter 1 The Generalized Assignment Problem - Springer
To prove the NP-completeness of the feasibility question, it is easy to design a reduction of an instance of problem Partition to an instance of GAP. Problem Partition, reputedly NP-complete, …
Lecture 11: NP-hard Scheduling Problems - Department of …
Lecture 11: NP-hard Scheduling Problems June 9th, 2009 We now show how to prove NP-hardness by illustrating it on 3 NP-hard scheduling problems. 1 (P2jjC max) We show this by …
Tensor Decompositions and Applications - University of …
speci c given tensor. The problem is NP-hard. Tensors may have di erent maximum and typical ranks. 1 The maximum rank is de ned as the largest attainable rank. 2 The typical rank is any …
csce750 — Analysis of Algorithms Fall 2020 — Lecture …
• L — problem you want to show is NP-hard The reduction must be an algorithm whose • input is instance of problem L′, and • output is an equivalent instance of problem L. 22 How to prove: …
Approximation Algorithms - CMU School of Computer …
Current best hardness result: Hastad shows 7/6 is NP-hard. Improved to 1.361 by Dinur and Safra. Beating 2-epsilon has been related to some other open problems (it is “unique games …
Subset Sum is NP-complete - Department of Computer …
Subset Sum is NP-complete The Subset Sum problem is as follows: given n non-negative integers w 1;:::;w n and a target sum W, the question is to decide if there is a subset I …
Notes for Lecture 16 1 Tractable and Intractable Problems
In other words, they are at least as hard as any other problem in NP; this is why they are called complete. Thus, if you could show that any one of the NP-complete problems that ... about the …
Module-5 : Backtracking
NP-Complete and NP-Hard problems 4.1. Basic concepts 4.2. Non-deterministic algorithms ... Problem definition: Find a subset of a given set A = {a 1 ... For example, for A = {1, 2, 5, 6, 8} …
Chapter 10
10.2.2 The general traveling salesman problem Definition: If an NP-complete problem can be solved in polynomial time then P = NP, else P ≠ NP. Definition: An algorithm for a given …
Intuitive Definitions of P, NP, NPC, NP-Hard - wmich.edu
As another example, any NP-complete problem is NP-hard. My favorite NP-complete problem is the Minesweeper problem. NP-easy In complexity theory, the complexity class NP-easy is the …
CMSC 451: The classes P and NP - CMU School of Computer …
Why, for example, is this true of Weighted Interval Scheduling? If you could solve the optimization version and got a solution of value M, then you could just check to see if M > C. If you can …
Graph Coloring - University of Illinois Urbana-Champaign
lems. For example, there is a coloring algorithm embedded in most compilers. Because the general problem can’t be solved efficiently, the implemented al-gorithms use limitations or …
1Traveling Salesperson Problem (TSP) - CMU School of …
1Traveling Salesperson Problem (TSP) The NP-hard Traveling Salesperson Problem (TSP) asks to nd the shortest route that visits all vertices in ... Step 1: Find some optimal substructure In …
NP Hardness/Completeness Overview - Duke University
–“Problem is in NP” (often a weak statement) –“The problem NP-Hard/Complete” (usually a strong statement) • Don’t reduce new problems to NP-hard complete problems if you meant to prove …
6.889 — Lecture 15: Traveling Salesman (TSP)
Traveling Salesman Problem (TSP) given G= (V;E) find a tour visiting each1 node v2V. NP–hard optimization problem, hard even for planar graphs Polynomial-time approximation for general …
1 MaxCut problem - University of Iowa
MaxCut problem is NP-complete. A weighted MaxCut is a general version of the problem where edges have weights. ... In this example Shas minimum size because the edges in the triangle …
A JOB SHOP SCHEDULING METHODS - DAAAM
solutions to "NP-hard" scheduling problems. The main disadvantage of branch and bound is that it is usually extremely time consuming, because the number of nodes one must consider is very …
10.1 Introduction - CMU School of Computer Science
Oct 12, 2005 · Definition 10.3.4 (Strongly NP-hard) A problem is strongly NP-hard if every problem in NP can be polynomially reduced to it in such a way that numbers in the reduced …
CS4234: Optimisation Algorithms Lecture 3 MIN-SET-COVER
Unfortunately, MIN-SET-COVER is NP-hard (i.e., NP-complete as a decision problem). See Example 2. below to see that MIN-VERTEX-COVER can be reduced to MIN-SET-COVER. In …
24 NP-Hard Problems
Algorithms Lecture 24: NP-Hard Problems 24.2 P, NP, and co-NP A decision problem is a problem whose output is a single boolean value: YES or NO.2 Let me define three classes of …
Lecture 8: NP Completeness - Rice University
This problem is in NP. Example 6 (k-Coloring Problem). Consider a graph representation of a map. G = (V,E), whose nodes are the partitions in the map and neighboring partitions ...
1 Minimum Vertex Cover - Stanford University
For example, in the following graph the size of ... The Vertex Cover problem is NP-hard, so we can not hope to solve it exactly. However, we can easily achieve a 2-approximation by …
1 (metric) Uncapacitated Facility Location - Khoury College of …
Example applications of facility locations include Hub and spoke scheduling; Locating concentrators in a routing network; Locating servers in a content-delivery network. Theorem 1. …
Lecture 24: Hardness Assumptions - CMU School of …
This decision problem is polynomial-time equivalent to the search problem. 4 Sparse-LPN Sparse-LPN is the same as LPN except all equations have only k 3 nonzero elements of a. We need to …
NP-complete Problems and Physical Reality - Scott Aaronson
and Taylor [24] posted a paper entitled “P=NP” to the arXiv. This paper argues that, since (1) finding a Steiner tree is NP-hard, (2) soap bubbles find a Steiner tree in polynomial time, (3) …
K-median Algorithms: Theory in Practice - Princeton …
Jain et al. [2] proved that the k-median problem is 1+ 2 e ˇ\1.736"-hard to approximate in a metric space. We note that, throughout this paper, all of our distance metrics satisfy the properties of …
Complexity and NP-completeness - MIT OpenCourseWare
Right: If P6˘NP. Definition. A problem is NP-complete if it is both NP-hard and in NP. Using the notion of NP-completeness, we can make an analogy between NP-hardness and big-O …
NP-hard Problems and Approximation Algorithms - The …
NP-hard Problems 5 equations dix = ci, i = 1,2,···,n, we obtain a representation of x through ci’s: xi = detDi/detD where D is a square submatrix of (AT,I)T and Di is a square matrix obtained from …
Session 21: Approximation Algorithms and Max-Cut - MIT …
8.1 The Max-Cut problem Unless the widely believed P 6= NP conjecture is false, there is no polynomial algorithm that can solve all instances of an NP-hard problem. Thus, when faced …
CS4234: Optimization Algorithms The Traveling Salesman
All the variants of the traveling salesman problem are NP-hard. In fact, the problem is NP-hard even for planar graphs with maximum degree 3. For the No-Repeats variants of the problem, …
NP-Hard and NP-Complete Problems - University of …
Chapter 9: NP-Hard And NP-Complete Problems NP-Hard and NP-Complete Problems For many of the problems we know and study, the best algorithms for their solution have computing times …
P vs. NP and Reductions - University of Washington
1. How to do a reduction (see the example/advice in slides 15-25) 2. To show a problem is NP-hard, you can reduce FROM 3-SAT, 3-coloring, or Hamiltonian Path TO your problem. (the …
NP-Completeness - Stanford University
NP-Hardness A language L is called NP-hard if for every L' ∈ NP, we have L' ≤ P L. A language in L is called NP-complete if L is NP-hard and L ∈ NP. The class NPC is the set of NP-complete …
Traveling salesman problem - Systems Engineering and …
The TSP problem belongs in the class of such problems known as NP-complete. Specifically, if one can find an efficient (i.e., polynomial-time) algorithm for the traveling salesman problem, …
Mixed-Integer Nonlinear Optimization: Introduction, …
MINLP is NP-hard: includes MILP, which are NP-hard [Kannan and Monma, 1978] Worse:MINLP are undecidable[Jeroslow, 1973]: ... Example: c(x) 0 convex, and 9i : c i(^x) >0, then 0 ^c i + …
1 De ning NP, co-NP, #P - Department of Computer Science
distinct; the most famous special case of this challenge is the \P versus NP" problem. 1 De ning NP, co-NP, #P Many important complexity classes can be de ned in terms computing the value …
Lecture Notes: Max-Coverage and Set-Cover (Greedy)
Observation: Suppose we can reduce Ato B. If Ais NP-hard, Bis also NP-hard. Remark: The notion of NP-hard can be extended to approximate problems as well. That is, we can show for …
NP-Completeness! - University of Washington
The Complexity Class NP-Hard NP-hard is the set of all problems to which every problem in NP can be reduced in polynomial time Example problem: Tower of Hanoi There are problems in …
1 The independent set problem - Princeton University
di cult) problem in coding theory, put forward by Claude Shannon [5]. Suppose you have an alphabet with a nite number of letters v 1;:::;v m. You want to transmit messages from this …
Exact Algorithms for NP-Hard Problems: A Survey - Texas …
How do we measure the quality of an exact algorithm for an NP-hard problem? Exact algorithms for NP-complete problems are sometimes hard to compare, since their analysis is done in …
Tractable problems Tractable and Intractable problems
NP complete and NP hard problems A problem Q is NP-hard if every problem in NP is reducible to Q; P <= Q A problem Q is NP – completeif it is NP-hard and is in NP. To show that a …
Contents Introduction - University of Chicago
De nition 2.11. A problem is NP-complete if it is both NP and NP-hard. Thus, NP-complete problems reduce to each other, and can be considered in certain ways to be equivalent. …
