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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. They showed that this problem is NP-hard even to approximate, and presented several heuristic algorithms. My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. In 2003 proved that it is still NP-hard and gave a polynomial-time algorithm with an approximation factor of 1nm. If one can establish a problem as NP-complete, there is strong reason to believe that it is intractable. Linear programming has been a successful tool in combinatorial optimization to achieve polynomial time algorithms for problems in P and also to achieve good approximation algorithms for problems which are NP-hard. Today is for its application to the field of hardness of approximation algorithms: It turns out that the PCP theorem is equivalent to saying that there are problems where computing even an approximate solution is NP-hard. This problem addresses the issue of timing when deploying viral campaigns. 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. This problem is known to be NP-hard even for alphabet of size 2. The reason the Cooper result holds is essentially that Bayes nets can be used to encode boolean satisfiability (SAT) problems, so solving the generic Bayes net inference problem lets you solve any SAT problem. In this problem, multiple missions compete for sensor resources. NP-complete problems are often addressed by using approximation algorithms. Both these problems are NP-hard, which motivates our interest in their approximation. We would then do better by trying to design a good approximation algorithm rather than searching endlessly seeking an exact solution.