Approximation Algorithms for NP-Hard Problems. Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems

ISBN: 0534949681,9780534949686 | 620 pages | 16 Mb

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Approximation Algorithms for NP-Hard Problems Dorit Hochbaum
Publisher: Course Technology

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. TOP 30 IMPORTANT QUESTION OF Design & Analysis of Algorithm(DAA) For GBTU/MMTU C.S./I.T. This book deals with designing polynomial time approximation algorithms for NP-hard optimization problems. 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. The story goes something like this: say you're working as a software developer and your boss gives you this project so I give up,” you need to show your boss that it's NP-Hard and this motivates the studying of reductions. 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. Explain NP-Complete and NP- Hard problem. One benefit of using Occam's Razor is that, if we're not One of the fascinating phenomenons of complexity is the dichotomy exhibited by many natural problems: they either have a polynomial-time algorithm (often with a low exponent) or are NP-hard, with very few examples in between. We would then do better by trying to design a good approximation algorithm rather than searching endlessly seeking an exact solution. It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. If one can establish a problem as NP-complete, there is strong reason to believe that it is intractable. Also Discuss What is meant by P(n)-approximation algorithm? My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. Khot's Unique Games Conjecture (UGC) states that a certain approximation problem (known as “Unique Games” or UG) is NP hard.

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