Author: S.N. KabadiPublisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 9
Book Description
An Efficient, Strongly Polynomial, E-approximation Parametric Optimization Scheme
Author: S.N. KabadiPublisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 9
Book Description
Parameterized Complexity and Polynomial-time Approximation Schemes
Author: Xiuzhen HuangPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
According to the theory of NPcompleteness, many problems that have important realworld applications are NPhard. This excludes the possibility of solving them in polynomial time unless P=NP. A number of approaches have been proposed in dealing with NPhard problems, among them are approximation algorithms and parameterized algorithms. The study of approximation algorithms tries to find good enough solutions instead of optimal solutions in polynomial time, while parameterized algorithms try to give exact solutions when a natural parameter is small. Inthis thesis, we study the structural properties of parameterized computation and approximation algorithms for NP optimization problems. In particular, we investigate the relationship between parameterized complexity and polynomialtime approximation scheme (PTAS) for NP optimization problems. We give nice characterizations for two important subclasses in PTAS: Fully Polynomial Time Approximation Scheme (FPTAS) and Effcient Polynomial Time Approximation Scheme (EPTAS), using the theory of parameterized complexity. Our characterization of the class FPTAS has its advantages over the former characterizations, and our characterization of EPTAS is the first systematic investigation of this new but important approximation class. We develop new techniques to derive strong computational lower bounds for certain parameterized problems based on the theory of parameterized complexity. For example, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the clique problem could not be solved in time O(f (k)n[superscript o(k)]) for any function f . This lower bound matches the upper bound of the trivial algorithm that simply enumerates and checks all subsets of k vertices in the given graph of n vertices. We then extend our techniques to derive computational lower bounds for PTAS and EPTAS algorithms of NP optimization problems. We prove that certain NP optimization problems with known PTAS algorithms have no PTAS algorithms of running time O(f (1/Epsilon)n [superscript o](1/[superscript Epsilon])) for any function f . Therefore, for these NP optimization problems, although theoretically they can be approximated in polynomial time to an arbitrarily small error bound Epsilon, they have no practically effective approximation algorithms for small error bound Epsilon. To our knowledge, this is the first time such lower bound results have been derived for PTAS algorithms. This seems to open a new direction for the study of computational lower bounds on the approximability of NP optimization problems.
Mathematical Reviews
Author: Rainbow of Computer Science
Author: Cristian S. CaludePublisher: Springer Science & Business Media
ISBN: 3642193900
Category : Computers
Languages : en
Pages : 290
Book Description
This volume is dedicated to Hermann Maurer on his 70th birthday. Topics include Automata, Formal Languages and Computability to various aspects of the Practice of Computer Science, as well as from Algorithmics to Learning.
Parametric Optimization and Related Topics
Author: Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 184
Book Description
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Author: Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
Author: Publisher: SIAM
ISBN: 9780898713664
Category : Mathematics
Languages : en
Pages : 608
Book Description
This text covers the proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, which was held in Atlanta, Georgia, in January 1996.
Handbook of Approximation Algorithms and Metaheuristics
Author: Teofilo F. GonzalezPublisher: CRC Press
ISBN: 1420010743
Category : Computers
Languages : en
Pages : 1434
Book Description
Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis. Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems.
Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques
Author: Klaus JansenPublisher: Springer
ISBN: 3540278214
Category : Computers
Languages : en
Pages : 436
Book Description
This book constitutes the joint refereed proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004 and the 8th International Workshop on Randomization and Computation, RANDOM 2004, held in Cambridge, MA, USA in August 2004. The 37 revised full papers presented were carefully reviewed and selected from 87 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, approximation classes, online problems, graph algorithms, cuts, geometric computations, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomised algorithms, randomized complexity theory, pseudorandomness, derandomization, probabilistic proof systems, error-correcting codes, and other applications of approximation and randomness.
Author: