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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

Khot's Unique Games Conjecture (UGC) states that a certain approximation problem (known as “Unique Games” or UG) is NP hard. NP, in the worst case, no polynomial-time algorithm guarantees a cover of cost [Math Processing Error] [2]. In 2003 proved that it is still NP-hard and gave a polynomial-time algorithm with an approximation factor of 1nm. The problem is NP hard for all non-trivial values of k and d and there are various approximation algorithms for solving this problem. Study of low-distortion embeddings (which can be pursued in a more general setting) has been a highly-active TCS research topic, largely due to its role in designing efficient approximation algorithms for NP-hard problems. (So to solve an instance of the Hitting Set Problem, it suffices to solve the instance of your problem with. 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. Equations are not displayed properly. Problem definition; Greedy algorithm; Remarks; Related; Bibliography. (This blog is about how to use randomized rounding to systematically derive greedy approximation algorithms and Lagrangian-relaxation algorithms. The Hitting Set problem is NP-hard [Karp' 72]. Here is a review of the Set Cover problem and the classic greedy algorithm for it. The Max-Cut problem is known to be NP-hard (if the widely believed {P\neq NP} conjecture is true this means that the problem cannot be solved in polynomial time).