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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems Dorit Hochbaum ebook
Publisher: Course Technology
ISBN: 0534949681, 9780534949686
Page: 620
Format: djvu

Sanjeev Arora is one of the architects of the Probabilistically Checkable Proofs (PCP) theorem, which revolutionized our understanding of complexity and the approximability of NP-hard problems. Authors: Chandra Computing it has been shown to be NP-hard [Thomassen 1989, 1993], and it is known to be fixed-parameter tractable. He helped create new approximation algorithms for fundamental optimization problems such as the Sparsest Cuts problem and the Euclidean Travelling Salesman problem, and contributed to the development of semi-definite programming as a practical algorithmic tool. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). These results He helped create new approximation algorithms for fundamental optimization problems such as the Sparsest Cuts problem and the Euclidean Travelling Salesman problem, and contributed to the development of semi-definite programming as a practical algorithmic tool. An infinitesimal advance in the traveling salesman problem breathes new life into the search for improved approximate solutions. This book deals with designing polynomial time approximation algorithms for NP-hard optimization problems. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. The theory of NP-completeness suggests that some problems in CS are inherently hard—that is, there is likely no possible algorithm that can efficiently solve them. Arora's research revolutionized the approach to essentially unsolvable problems that have long bedeviled the computing field, the so-called NP-complete problems. Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. One standard approach to tractably solving an NP-hard problem is to find another algorithm with an approximation guarantee. Title: Approximation algorithms for Euler genus and related problems. The computer scientist Richard Karp, of the University of California at Berkeley, showed that the traveling salesman problem is “NP-hard,” which means that it has no efficient algorithm (unless a famous conjecture called P=NP is true — but the majority of computer scientists now suspect that it is false).