Download or read book Efficient Approximation Algorithms for Geometric Packing and Covering Problems written by Srinivas Rao Doddi and published by . This book was released on 2000 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Approximation Algorithms for Geometric Packing Problems written by Lars Dennis Prädel and published by . This book was released on 2012 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Ashish Goel and published by Springer. This book was released on 2008-08-28 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the 11th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2008) and the 12th International Workshop on Randomization and Computation (RANDOM 2008), which took place concurrently at the MIT (M- sachusetts Institute of Technology) in Boston, USA, during August 25–27, 2008. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 11th in the series after Aalborg (1998), Berkeley (1999), Saarbru ̈cken (2000), Berkeley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 12th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). Topics of interest for APPROX and RANDOM are: design and analysis of - proximation algorithms, hardness of approximation, small space, sub-linear time, streaming, algorithms, embeddings and metric space methods, mathematical programming methods, combinatorial problems in graphs and networks, game t- ory, markets, economic applications, geometric problems, packing, covering, scheduling, approximate learning, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and - beddings, error-correcting codes, average-case analysis, property testing, com- tational learning theory, and other applications of approximation and randomness.
Download or read book Approximation Algorithms for Geometric Covering Problems for Disks and Squares written by Nan Hu and published by . This book was released on 2013 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric covering is a well-studied topic in computational geometry. We study three covering problems: Disjoint Unit-Disk Cover, Depth-([lto]K) Packing and Red-Blue Unit-Square Cover.
Download or read book Improved Approximation Algorithms for Geometric Packing Problems with Experimental Evaluation written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Michel Goemans and published by Springer. This book was released on 2001-08-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 4th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2001 and of the 5th International Workshop on Ranomization and Approximation Techniques in Computer Science, RANDOM 2001, held in Berkeley, California, USA in August 2001. The 26 revised full papers presented were carefully reviewed and selected from a total of 54 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, on-line problems, randomization, de-randomization, average-case analysis, approximation classes, randomized complexity theory, scheduling, routing, coloring, partitioning, packing, covering, computational geometry, network design, and applications in various fields.
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 and Online Algorithms written by Jarosław Byrka and published by Springer Nature. This book was released on 2023-12-21 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Workshop on Approximation and Online Algorithms, WAOA 2023, held in Amsterdam, The Netherlands, during September 7–8, 2023 The 16 full papers included in this book are carefully reviewed and selected from 43 submissions. The topics of WAOA 2023 were algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT-approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, resource augmentation, and scheduling problems
Download or read book Algorithms ESA 2005 written by Gerth S. Brodal and published by Springer Science & Business Media. This book was released on 2005-09-19 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th Annual European Symposium on Algorithms, ESA 2005, held in Palma de Mallorca, Spain, in September 2005 in the context of the combined conference ALGO 2005. The 75 revised full papers presented together with abstracts of 3 invited lectures were carefully reviewed and selected from 244 submissions. The papers address all current issues in algorithmics reaching from design and mathematical issues over real-world applications in various fields up to engineering and analysis of algorithms.
Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
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 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:
Download or read book Algorithms for Geometric Covering and Piercing Problems written by Robert Fraser and published by . This book was released on 2012 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis involves the study of a range of geometric covering and piercing problems, where the unifying thread is approximation using disks. While some of the problems addressed in this work are solved exactly with polynomial time algorithms, many problems are shown to be at least NP-hard. For the latter, approximation algorithms are the best that we can do in polynomial time assuming that P is not equal to NP. One of the best known problems involving unit disks is the Discrete Unit Disk Cover (DUDC) problem, in which the input consists of a set of points P and a set of unit disks in the plane D, and the objective is to compute a subset of the disks of minimum cardinality which covers all of the points. Another perspective on the problem is to consider the centre points (denoted Q) of the disks D as an approximating set of points for P. An optimal solution to DUDC provides a minimal cardinality subset Q*, a subset of Q, so that each point in P is within unit distance of a point in Q*. In order to approximate the general DUDC problem, we also examine several restricted variants. In the Line-Separable Discrete Unit Disk Cover (LSDUDC) problem, P and Q are separated by a line in the plane. We write that l^- is the half-plane defined by l containing P, and l^+ is the half-plane containing Q. LSDUDC may be solved exactly in O(m^2n) time using a greedy algorithm. We augment this result by describing a 2-approximate solution for the Assisted LSDUDC problem, where the union of all disks centred in l^+ covers all points in P, but we consider using disks centred in l^- as well to try to improve the solution. Next, we describe the Within-Strip Discrete Unit Disk Cover (WSDUDC) problem, where P and Q are confined to a strip of the plane of height h. We show that this problem is NP-complete, and we provide a range of approximation algorithms for the problem with trade-offs between the approximation factor and running time. We outline approximation algorithms for the general DUDC problem which make use of the algorithms for LSDUDC and WSDUDC. These results provide the fastest known approximation algorithms for DUDC. As with the WSDUDC results, we present a set of algorithms in which better approximation factors may be had at the expense of greater running time, ranging from a 15-approximate algorithm which runs in O(mn + m log m + n log n) time to a 18-approximate algorithm which runs in O(m^6n+n log n) time. The next problems that we study are Hausdorff Core problems. These problems accept an input polygon P, and we seek a convex polygon Q which is fully contained in P and minimizes the Hausdorff distance between P and Q. Interestingly, we show that this problem may be reduced to that of computing the minimum radius of disk, call it k_opt, so that a convex polygon Q contained in P intersects all disks of radius k_opt centred on the vertices of P. We begin by describing a polynomial time algorithm for the simple case where P has only a single reflex vertex. On general polygons, we provide a parameterized algorithm which performs a parametric search on the possible values of k_opt. The solution to the decision version of the problem, i.e. determining whether there exists a Hausdorff Core for P given k_opt, requires some novel insights. We also describe an FPTAS for the decision version of the Hausdorff Core problem. Finally, we study Generalized Minimum Spanning Tree (GMST) problems, where the input consists of imprecise vertices, and the objective is to select a single point from each imprecise vertex in order to optimize the weight of the MST over the points. In keeping with one of the themes of the thesis, we begin by using disks as the imprecise vertices. We show that the minimization and maximization versions of this problem are NP-hard, and we describe some parameterized and approximation algorithms. Finally, we look at the case where the imprecise vertices consist of just two vertices each, and we show that the minimization version of the problem (which we call 2-GMST) remains NP-hard, even in the plane. We also provide an algorithm to solve the 2-GMST problem exactly if the combinatorial structure of the optimal solution is known. We identify a number of open problems in this thesis that are worthy of further study. Among them: Is the Assisted LSDUDC problem NP-complete? Can the WSDUDC results be used to obtain an improved PTAS for DUDC? Are there classes of polygons for which the determination of the Hausdorff Core is easy? Is there a PTAS for the maximum weight GMST problem on (unit) disks? Is there a combinatorial approximation algorithm for the 2-GMST problem (particularly with an approximation factor under 4)?
Download or read book Efficient Approximation and Online Algorithms written by Evripidis Bampis and published by Springer Science & Business Media. This book was released on 2006-02-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good opportunity for computer science practitioners and researchers to get in sync with current state-of-the-art and future trends in the field of combinatorial optimization and online algorithms. Recent advances in this area are presented focusing on the design of efficient approximation and on-line algorithms. One central idea in the book is to use a linear program relaxation of the problem, randomization and rounding techniques.
Download or read book Fast Approximation Algorithms for Fractional Packing and Covering Problems written by S. Plotkin and published by . This book was released on 1992 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give several applications of our algorithms. The new approach yields several orders of magnitude of improvement over the best previously known running times for the scheduling of unrelated parallel machines in both the preemptive and the non-preemptive models, for the job shop problem, for the cutting-stock problem, and for the minimum cost multicommodity flow problem.
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.
