Download or read book Approximation Algorithms for Partial Covering Problems written by Rajiv Gandhi and published by . This book was released on 2001 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the generalization of covering problems to partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-set cover, if each element occurs in at most f sets, then we derive a primal-dual f-approximation algorithm (thus implying a 2-approximation for k-vertex cover) in polynomial time. In addition to its simplicity, this algorithm has the advantage of being parallelizable. For instances where each set has cardinality at most three, we obtain an approximation of 4/3. We also present better than 2-approximation algorithms for k-vertex cover on bounded degree graphs, and for vertex cover on expanders of bounded average degree. We obtain a polynomial-time approximation scheme for k-vertex cover on planar graphs, and for covering points in Rd̂ by disks.
Download or read book Approximation Algorithms for Partial Capacitated Covering Problems written by Guy Flysher and published by . This book was released on 2007 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Algorithms for Combinatorial Optimization written by Klaus Jansen and published by Springer. This book was released on 2003-06-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, held in Rome, Italy in September 2002. The 20 revised full papers presented were carefully reviewed and selected from 54 submissions. Among the topics addressed are design and analysis of approximation algorithms, inapproximability results, online problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and other fields.
Download or read book Approximation Algorithms written by Vijay V. Vazirani and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Approximation Algorithms for Covering Problems written by Christos Koufogiannakis and published by . This book was released on 2009 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Then we show distributed versions of the sequential algorithm. For W EIGHTED VERTEX COVER, we give a distributed 2-approximation algorithm taking O (log n) rounds. The algorithm generalizes to covering mixed integer linear programs (CMIP) with two variables per constraint ([Delta] = 2). For any MONOTONE COVERING problem, we show a distributed [Delta]-approximation algorithm taking O (log 2 [Special characters omitted.]) rounds, where [Special characters omitted.] is the number of constraints. Last, we extend the distributed algorithms for covering to compute [Delta]-approximate solutions for FRACTIONAL PACKING and M AXIMUM WEIGHTED b-MATCHING in hypergraphs, where [Delta] is the maximum number of packing constraints in which a variable appears (for MAXIMUM WEIGHTED b-MATCHING [Delta] is the maximum edge degree--for graphs [Delta] = 2).
Download or read book Approximation Algorithms for NP hard Problems written by Dorit S. Hochbaum and published by Course Technology. This book was released on 1997 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Approximation and Online Algorithms written by Giuseppe Persiano and published by Springer. This book was released on 2005-02-09 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd Workshop on Approximation and Online Algorithms (WAOA 2004) focused on the design and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications arising from a variety of ?elds. WAOA 2004 took place in Bergen, Norway, from September 14 to September 16, 2004. The workshop was part of the ALGO 2004 event which also hosted ESA, WABI, IWPEC, and ATMOS. TopicsofinterestsforWAOA2004were:applicationstogametheory,appr- imation classes, coloring and partitioning, competitive analysis, computational ?nance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, routing, packing and covering, paradigms, randomization techniques, and scheduling problems. In response to our call we received 47 submissions. Each submission was reviewed by at least 3 referees, who judged the paper on originality, quality, and consistency with the topics of the conference. Based on the reviews, the Program Committee selected 21 papers. This volume contains the 21 selected papers and the two invited talks given by Yossi Azar and Klaus Jansen. We thank all the authors who submitted papers to the workshop and we also kindly thank the local organizers of ALGO 2004.
Download or read book The Design of Approximation Algorithms written by David P. Williamson and published by Cambridge University Press. This book was released on 2011-04-26 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Approximation Algorithms for Covering Problems written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Design and Analysis of Approximation Algorithms written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2011-11-18 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way.
Download or read book Computational Experience with Approximation Algorithms for the Set Covering Problems written by Mekhon Ṿaitsman le-madaʻ. Department of Applied Mathematics and Computer Science and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Approximation Algorithms and Metaheuristics written by Teofilo F. Gonzalez and published by CRC Press. This book was released on 2018-05-15 with total page 840 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Approximation Algorithms and Metaheuristics, Second Edition reflects the tremendous growth in the field, over the past two decades. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability. Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks (sensor and wireless), communication, bioinformatics search, streams, virtual communities, and more. About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph.D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma, the Pennsylvania State University, and the University of Texas at Dallas, before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.
Download or read book Approximation and Online Algorithms written by Giuseppe Persiano and published by Springer Science & Business Media. This book was released on 2005-02-23 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post proceedings of the Second International Workshop on Approximation and Online Algorithms, WAOA 2004, held in Bergen, Norway in September 2004. The 21 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement from 47 submissions. WAOA is devoted to the design and analysis of algorithms for online and computationally hard problems. Among the topics addressed are applications to game theory, approximation classes, coloring and partitioning, competitive analysis, computational finance, cuts and connectivity, geometric computations, inapproximability results, mechanism design, network design, routing, packing and covering, paradigms, randomization techniques, and scheduling problems.
Download or read book Iterative Methods in Combinatorial Optimization written by Lap Chi Lau and published by Cambridge University Press. This book was released on 2011-04-18 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.
Download or read book Geometric Approximation Algorithms written by Sariel Har-Peled and published by American Mathematical Soc.. This book was released on 2011 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Download or read book Some Exact and Approximation Algorithms for Packing and Covering Problems written by Gregory Chase Dobson and published by . This book was released on 1981 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Chandra Chekuri and published by Springer. This book was released on 2005-08-25 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2005) and the 9th International Workshop on Randomization and Computation (RANDOM 2005), which took place concurrently at the University of California in Berkeley, on August 22 –24, 2005.
