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

In the Traveling Salesman is an NP-Hard problem. It seems like there would be incentive to participate if players believed their approximation algorithm or embedding scheme could beat the next firm's. Pricing such an instrument involves solving an NP-complete problem, but no one would argue that this implies anything about real financial instruments. Due to the connection between approximation algorithms and computational optimization problems, reductions which preserve approximation in some respect are for this subject preferred than the usual Turing and Karp reductions. The study of approximation algorithms for NP-hard problems has blossomed into a rich field, especially as a result of intense work over the last two decades. Approximation Algorithm vs Heuristic. The authors give another, similarly artificial, example: Consider for example a . Abraham Flaxman | October 16, 2009 at 3:25 pm | Permalink. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. Approximation algorithm: identifies approximate solutions to problems (mostly often NP-complete and NP-hard problems) to a certain bound. Note that hardness relations are always with respect to some reduction. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. Currently we have approximation algorithms that can come up with “good solutions” in a fairly acceptable amount of time.