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Approximation Algorithms for NP-Hard Problems Dorit Hochbaum
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Approximation algorithms for NP-hard problems. I normally do machine learning work, and when I'm evaluating an algorithm on a data set, I always use cross-validation to determine how effective the. Abraham Flaxman | October 16, 2009 at 3:25 pm | Permalink. Pricing such an instrument involves solving an NP-complete problem, but no one would argue that this implies anything about real financial instruments. When an NP-complete problem must be solved, one approach is to use a polynomial algorithm to approximate the solution; the answer thus obtained will not necessarily be optimal but will be reasonably close. Khot's Unique Games Conjecture (UGC) —which asserts the NP-hardness of approximating a very simple constraint satisfaction problem— has assumed a central role in the effort to understand the optimal approximation ratios achievable for various NP-hard problems. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. 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. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). A less obvious application is that the minimum spanning tree can be used to approximately solve the traveling salesman problem. The past few years have seen a flurry of results, including surprises such as a subexponential-time approximation algorithm, as well as algorithms for all “natural” families of instances we can think of. €� traveling salesperson problem, Steiner tree. It seems like there would be incentive to participate if players believed their approximation algorithm or embedding scheme could beat the next firm's. The Max-Cut problem is known to be NP-hard (if the widely believed {P\neq NP} conjecture is true this means that the problem cannot be solved in polynomial time). Yet most such problems are NP-hard. Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. The authors give another, similarly artificial, example: Consider for example a .