Last edited by Goltilrajas

Tuesday, July 28, 2020 | History

11 edition of **Approximation Algorithms for NP-Hard Problems** found in the catalog.

- 371 Want to read
- 30 Currently reading

Published
**July 26, 1996**
by Course Technology
.

Written in English

- Mathematical theory of computation,
- Programming (Mathematics),
- Linear Programming,
- Mathematics,
- Computers - Languages / Programming,
- Science/Mathematics,
- Programming Languages - General,
- Discrete Mathematics,
- Computers / Computer Science,
- Algorithms,
- Approximation Theory

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 624 |

ID Numbers | |

Open Library | OL7786857M |

ISBN 10 | 0534949681 |

ISBN 10 | 9780534949686 |

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 : $ P, NP-Problems • Class NP (Non-deterministic Polynomial) is the class of decision problems that can be solved by non-deterministic polynomial algorithms. • Note that all problems in Class P are in Class NP: We can replace the non-deterministic guessing of Stage 1 with the deterministic algorithm for the decision problem, and then in Stage 2.

In this chapter we introduce the important concept of approximation algorithms. So far we have dealt mostly with polynomially solvable problems. In the remaining chapters we shall indicate some strategies to cope with NP-hard combinatorial optimization problems. Here approximation algorithms must be mentioned in the first place. Let me mention some of the biggest open problems in approximation algorithms/hardness of approximation. For simplicity, I will try to be less formal with the definitions and the problems. 1. Unique games conjecture: Resolving this famous conjectur.

Most combinatorial optimization problems are NP-hard to solve optimally. A natural approach to cope with this intractability is to design an “approximation algorithm” – an eﬃcient algorithm that is guaranteed to produce a good approximation to the optimum solution. The last two decades has witnessed tremendous developments in the design ofFile Size: 2MB. Interesting fact: nobody knows any algorithm with approximation ratio Best known is 2 − O(1/ √ logn), which is 2 −o(1). Current best hardness result: Hastad shows 7/6 is NP-hard. Improved to by Dinur and Safra. Beating 2-epsilon has been related to some other open problems (it is “unique games hard”), but is not known to be File Size: 88KB.

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Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. This book is actually a collection of survey articles written by some of the foremost experts in this field.5/5(1). Klein P and Young N Approximation algorithms for NP-hard optimization problems Algorithms and theory of computation handbook, () Misra N, Narayanaswamy N, Raman V and Shankar B Solving MINONESSAT as fast as VERTEX COVER Proceedings of the 35th international conference on Mathematical foundations of computer science, ().

The first part of the book presents a set of classical NP hard problems, set covering, bin packing, knapsack, etc.

and their approximation algorithms. These algorithms are extracted from a number of fundamental papers, which are of long, delicate presentations.

Vazirami presented the problems and solutions in a unified by: Approximation Algorithms for NP-Hard Problems Edited by Dorit S. Hochbaum Published July The thirteen chapters of the book are written by leading researchers that have contributed to the state of the art of approximation algorithms.

About the book. Table of Contents. ISBN: OCLC Number: Description: xxii, pages: illustrations ; 24 cm: Contents: Approximation algorithm for scheduling / Leslie A.

Hall --Approximation algorithms for bin packing: a survey / E.G. Coffmann, Jr., M.R. Garey, and D.S. Johnson --Approximating covering and packing problems: set cover, vertex cover. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms/5(12).

Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. Too frequently, when attempting to get a solution for a problem, one is confronted with the fact that the problem is : S HochbaDorit.

From the introduction: This book deals with designing polynomial time approximation algorithms for NP-hard optimization problems. Typically, the decision versions of these problems are in NP, and are therefore NP-complete.

From the viewpoint of exact solutions, all NP-complete problems are equally hard, since they are inter-reducible via polynomial time reductions. 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.

Although this may seem a paradox, all exact science is dominated by the idea of approximation. Bertrand Russell () Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed con jecture that P -=/= NP, their exact solution is prohibitively time consuming/5.

Although this may seem a paradox, all exact science is dominated by the idea of approximation. Bertrand Russell () Most natural optimization problems, including those arising in important application areas, are NP-hard.

Therefore, under the widely believed con jecture that P -=/= NP, their exact solution is prohibitively time consuming.4/5(4). Approximation Algorithms for NP-Hard P roblems algorithms that are eﬃcient in rela tively small inputs, may become impractica l for input sizes of sev eral gigabytes.

approximate solutions to NP-hard discrete optimization problems. At one or two points in the book, we do an NP-completeness reduction to show that it can be hard to ﬁnd approximate solutions to such problems; we include a short appendix on the problem class NP and the notion of NP-completeness for those unfamiliar with the concepts.

Yet most interesting discrete optimization 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.

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 5/5(2). Furthermore, for many natural NP-hard optimization problems, approximation algorithms have been developed whose accuracy nearly matches the best achievable according to the theory of NP-completeness.

Thus optimization problems can be cate-gorized according to the best accuracy achievable by a polynomial-time approximation algorithm for each. 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. NP-hard problems, a central question is whether we can efﬁciently compute Good approximation algorithms have bee n proposed for some key problems.

One corollary of this theorem is that a. 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 Author: Dorit Hochbaum. Approximation Algorithms: For many NP-complete problems there are approximation algorithms that are fast and give an answer that is close to the optimal (e.g., within twice).

There are also lower bounds as well. Some of these algorithms are useable in the real world. a polynomial-time asymptotically optimal approximation algorithm. For all of the above problems, our results improve on the best previous approximation algorithms or schemes, which are: (1) applications of the Lipton–Tarjan planar separator theorem to minimum vertex cover [Bar-Yehuda and Even, ; Chiba et al., ] and to.Furthermore, for many natural NP-hard optimization problems, approximation algorithms have been developed whose accuracy nearly matches the best achievable according to the theory of NP-completeness.

Thus optimization problems can be cate-gorized according to the best accuracy achievable by a polynomial-time approximation algorithm for each File Size: KB.NP-hard problems vary greatly in their approximability; some, such as the knapsack problem, can be approximated within a multiplicative factor +, for any fixed >, and therefore produce solutions arbitrarily close to the optimum (such a family of approximation algorithms is called a polynomial time approximation scheme or PTAS).