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

I'm enjoying reading notes from Shuchi Chawla's course at the University of Wisconsin, Madison on approximation algorithms for NP-hard optimization problems. 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. With Christos Papadimitriou in 1988, he framed the systematic study of approximation algorithms for {mathsf{NP}} -hard optimization problems around the classes {mathsf{MaxNP}} and {mathsf{MaxSNP}} . Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. Different approximation algorithms have their advantages and disadvantages. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. This paper deals with firefighter problem on rooted trees. Have you ever wondered if a specific NP-hard problem has an approximation algorithm or not? Comparing Algorithms for the Traveling Salesman Problem. 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. It is known that the firefighter problem is NP-hard even for rooted trees of maximum degree 3. 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]. Note that hardness relations are always with respect to some reduction. 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. The traveling salesman problem (TSP) is an NP-complete problem. If yes, you may like to visit this site: A Compendium of NP optimization problems. We propose techniques to improve a given approximation algorithm. They couldn't use a quick approximation algorithm for subset-sum, since they needed the sum to be exactly equal to their target amount. 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.