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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. 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). Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. 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. Perhaps, the best source on approximation algorithms. Year of my PhD studies at the U of Alberta where I study the theory behind efficient algorithms for combinatorial optimization problems. An infinitesimal advance in the traveling salesman problem breathes new life into the search for improved approximate solutions. Optimization/approximation algorithms/polynomial time/ NP-HARD. Approximation Algorithm for NP-hard problems by Dorit Hochbaum is a set of chapters by different contributors. Think too hard about approximation algorithms. They show roughly “if you have a problem for which each and every alpha approximation to the optimum is goodish, then here is a 1-line algorithm that will solve that problem perfectly.” Everyone is familiar with the notion of reduction in complexity theory … essentially a certificate that your problem instance might (in the worst case) be encoding an NP-complete problem. It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. Most of the problems I study are NP-hard so I focus mainly on approximation algorithms.