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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. Many combinatorial optimization problems can be expressed as the minimization or maximization of a submodular function, including min- and max-cut, coverage problems, and welfare maximization in algorithmic game theory. Unsurprisingly, submodular maximization tends to be NP-hard for most natural choices of constraints, so we look for approximation algorithms. My answer is that is it ignores randomized and approximation algorithms. An infinitesimal advance in the traveling salesman problem breathes new life into the search for improved approximate solutions. 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. Because all of these problems are NP-hard, the primary goal of this research is to produce polynomial-time, approximation algorithms for each problem considered. Product Description This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. Even if P is not equal to NP, there may be randomized algorithms (either Monte Carlo or Las Vegas) that can answer NP hard problems rapidly. It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. 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). Problem classes P, NP, NP-hard and NP-complete, deterministic and non deterministic polynomial time algorithms., Approximation algorithms for some NP-complete problems.