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Approximation Algorithms for NP-Hard Problems book

Approximation Algorithms for NP-Hard Problems book

Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems



Download Approximation Algorithms for NP-Hard Problems




Approximation Algorithms for NP-Hard Problems Dorit Hochbaum ebook
Publisher: Course Technology
Page: 620
ISBN: 0534949681, 9780534949686
Format: djvu


Different approximation algorithms have their advantages and disadvantages. It is known that the firefighter problem is NP-hard even for rooted trees of maximum degree 3. SAT (boolean satisfiability, the "canonical" NP-hard problem) is a really tough nut to crack, whereas for example euclidean TSP (traveling salesman) is hard to solve optimally but has simple and fast algorithms that guarantee to solve it to within a constant factor of the optimum. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. Note that hardness relations are always with respect to some reduction. This paper deals with firefighter problem on rooted trees. Optimization/approximation algorithms/polynomial time/ NP-HARD. The traveling salesman problem (TSP) is an NP-complete problem. Comparing Algorithms for the Traveling Salesman Problem. 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. Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. A simple factor-2 approximation just walks around the spanning tree and can be computed in O(n log n) time with simple algorithms! Yet most such problems are NP-hard. Many of the striking advances in theoretical computer science over the past two decades concern approximation algorithms, which compute provably near-optimal solutions to NP-hard optimization problems. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. We propose techniques to improve a given approximation algorithm. 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.

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