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

Abraham Flaxman | October 16, 2009 at 3:25 pm | Permalink. It seems like there would be incentive to participate if players believed their approximation algorithm or embedding scheme could beat the next firm's. Problem classes P, NP, NP-hard and NP-complete, deterministic and non deterministic polynomial time algorithms., Approximation algorithms for some NP-complete problems. The authors give another, similarly artificial, example: Consider for example a . This is one of Karp's original NP-complete problems. Think too hard about approximation algorithms. Because all of these problems are NP-hard, the primary goal of this research is to produce polynomial-time, approximation algorithms for each problem considered. Pricing such an instrument involves solving an NP-complete problem, but no one would argue that this implies anything about real financial instruments. I'm enjoying reading notes from Shuchi Chawla's course at the University of Wisconsin, Madison on approximation algorithms for NP-hard optimization problems. Instead of trying to solve this problem exactly, we will reason about whether constant factor approximation algorithms exist, i.e. For graduate-level courses in approximation algorithms. The expected value of a discrete random variable). It assumes familiarity with algorithms, mathematical proofs about the correctness of algorithms, probability theory and NP-completeness. 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. Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. 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. 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. Finally, we assume that the reader knows something about NP-completeness, at least enough to know that there might be good reason for wanting fast, approximate solutions to NP-hard discrete optimization problems. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ).