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Approximation Algorithms for NP-Hard Problems
Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems

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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) —which asserts the NP-hardness of approximating a very simple constraint satisfaction problem— has assumed a central role in the effort to understand the optimal approximation ratios achievable for various NP-hard problems. Approximation Algorithm for NP-hard problems by Dorit Hochbaum is a set of chapters by different contributors. Year of my PhD studies at the U of Alberta where I study the theory behind efficient algorithms for combinatorial optimization problems. In Part I, we learned of an instance of the NP-complete problem subset-sum [1] that was solved by three lawyers on an episode of the USA Network show Suits [2]. The problem was to go through a set of deposits made to five banks in Liechtenstein one of the lawyers, the team solved the problem in a relatively short length of time. Most of the problems I study are NP-hard so I focus mainly on approximation algorithms. Problem classes P, NP, NP-hard and NP-complete, deterministic and nondeterministic polynomial time algorithms., Approximation algorithms for some NP complete problems. Arora's research revolutionized the approach to essentially unsolvable problems that have long bedeviled the computing field, the so-called NP-complete problems. The past few years have seen a flurry of results, including surprises such as a subexponential-time approximation algorithm, as well as algorithms for all “natural” families of instances we can think of. They couldn't use a quick approximation algorithm for subset-sum, since they needed the sum to be exactly equal to their target amount. Perhaps, the best source on approximation algorithms. 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.

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