Parameterized Algorithms

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Parameterized Algorithms

Parameterized Algorithms written by Marek Cygan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-20 with Computers categories.

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.

Kernelization

Kernelization written by Fedor V. Fomin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-10 with Computers categories.

A complete introduction to recent advances in preprocessing analysis, or kernelization, with extensive examples using a single data set.

Invitation To Fixed Parameter Algorithms

Invitation To Fixed Parameter Algorithms written by Rolf Niedermeier and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-02 with Mathematics categories.

This research-level text is an application-oriented introduction to the growing and highly topical area of the development and analysis of efficient fixed-parameter algorithms for optimally solving computationally hard combinatorial problems. The book is divided into three parts: a broad introduction that provides the general philosophy and motivation; followed by coverage of algorithmic methods developed over the years in fixed-parameter algorithmics forming the core of the book; and a discussion of the essentials from parameterized hardness theory with a focus on W[1]-hardness which parallels NP-hardness, then stating some relations to polynomial-time approximation algorithms, and finishing up with a list of selected case studies to show the wide range of applicability of the presented methodology. Aimed at graduate and research mathematicians, programmers, algorithm designers, and computer scientists, the book introduces the basic techniques and results and provides a fresh view on this highly innovative field of algorithmic research.

Algorithms And Data Structures

Algorithms And Data Structures written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Algorithms categories.

Parameterized Algorithms And Computational Lower Bounds

Parameterized Algorithms And Computational Lower Bounds written by Ge Xia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Many problems of practical significance are known to be [subscript] NP-hard, and hence, are unlikely to be solved by polynomial-time algorithms. There are several ways to cope with the [subscript] NP-hardness of a certain problem. The most popular approaches include heuristic algorithms, approximation algorithms, and randomized algorithms. Recently, parameterized computation and complexity have been receiving a lot of attention. By taking advantage of small or moderate parameter values, parameterized algorithms provide new venues for practically solving problems that are theoretically intractable. In this dissertation, we design efficient parameterized algorithms for several wellknown [subscript] NP-hard problems and prove strong lower bounds for some others. In doing so, we place emphasis on the development of new techniques that take advantage of the structural properties of the problems. We present a simple parameterized algorithm for Vertex Cover that uses polynomial space and runs in time O(1.2738 [superscript] k + kn). It improves both the previous O(1.286 [superscript] k + kn)-time polynomial-space algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745 [superscript] kk4 + kn)-time exponential-space algorithm, by Chandran and Grandoni. This algorithm stands out for both its performance and its simplicity. Essential to the design of this algorithm are several new techniques that use structural information of the underlying graph to bound the search space. For Vertex Cover on graphs with degree bounded by three, we present a still better algorithm that runs in time O(1.194[superscript] k + kn), based on an "almost-global" analysis of the search tree. We also show that an important structural property of the underlying graphs the graph genus-largely dictates the computational complexity of some important graph problems including Vertex Cover, Independent Set and Dominating Set. We present a set of new techniques that allows us to prove almost tight computationl lower bounds for some [subscript] NP-hard problems, such as Clique, Dominating Set, Hitting Set, Set Cover, and Independent Set. The techniques are further extended to derive computational lower bounds on polynomial time approximation schemes for certain [subscript] NP-hard problems. Our results illustrate a new approach to proving strong computational lower bounds for some [subscript] NP-hard problems under reasonable conditions.

Algorithms And Complexity

Algorithms And Complexity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Algorithms categories.

Parameterized And Exact Computation

Parameterized And Exact Computation written by Dániel Marx and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-09 with Computers categories.

This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Symposium on Parameterized and Exact Computation, IPEC 2011, in Saarbrücken, Germany, in September 2011. The 21 revised full papers presented were carefully reviewed and selected from 40 submissions. The topics addressed cover research in all aspects of parameterized and exact computation and complexity, including but not limited to new techniques for the design and analysis of parameterized and exact algorithms, fixed-parameter tractability results, parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications, applications of parameterized and exact computation, and implementation issues of parameterized and exact algorithms.

Algorithms

Algorithms written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computer algorithms categories.

Randomized And Deterministic Parameterized Algorithms And Their Applications In Bioinformatics

Randomized And Deterministic Parameterized Algorithms And Their Applications In Bioinformatics written by Songjian Lu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

Parameterized NP-hard problems are NP-hard problems that are associated with special variables called parameters. One example of the problem is to find simple paths of length k in a graph, where the integer k is the parameter. We call this problem the p-path problem. The p-path problem is the parameterized version of the well-known NP-complete problem - the longest simple path problem. There are two main reasons why we study parameterized NP-hard problems. First, many application problems are naturally associated with certain parameters. Hence we need to solve these parameterized NP-hard problems. Second, if parameters take only small values, we can take advantage of these parameters to design very effective algorithms. If a parameterized NP-hard problem can be solved by an algorithm of running time in form of f(k)n^O(1), where k is the parameter, f(k) is independent of n, and n is the input size of the problem instance, we say that this parameterized NP-hard problem is fixed parameter tractable (FPT). If a problem is FPT and the parameter takes only small values, the problem can be solved efficiently (it can be solved almost in polynomial time). In this dissertation, first, we introduce several techniques that can be used to design efficient algorithms for parameterized NP-hard problems. These techniques include branch and bound, divide and conquer, color coding and dynamic programming, iterative compression, iterative expansion and kernelization. Then we present our results about how to use these techniques to solve parameterized NP-hard problems, such as the p-path problem and the pd-feedback vertex set problem. Especially, we designed the first algorithm of running time in form of f(k)n^O(1) for the pd-feedback vertex set problem. Thus solved an outstanding open problem, i.e. if the pd-feedback vertex set problem is FPT. Finally, we will introduce how to use parameterized algorithm techniques to solve the signaling pathway problem and the motif finding problem from bioinformatics.

Graph Theoretic Concepts In Computer Science

Graph Theoretic Concepts In Computer Science written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algorithms categories.