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Approximation Algorithms for NP-Hard Problems Dorit Hochbaum
Publisher: Course Technology

One standard approach to tractably solving an NP-hard problem is to find another algorithm with an approximation guarantee. There are already arbitrarily good polynomial-time approximation algorithms for many NPO-complete problems like TSP, but TSP is actually APX-complete too, meaning you cannot even approximate answers beyond a certain factor unless P=NP. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. Yet most such problems are NP-hard. 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]. Product Description This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. They couldn't use a quick approximation algorithm for subset-sum, since they needed the sum to be exactly equal to their target amount. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. 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. I still maintain that someone could make a good movie with the premise "random guy finds easy algorithm to solve NP-complete problems now what?" in the vein of Primer (random guys . 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.