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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

If one can establish a problem as NP-complete, there is strong reason to believe that it is intractable. My answer is that is it ignores randomized and approximation algorithms. Moreover, we prove that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms. I'm enjoying reading notes from Shuchi Chawla's course at the University of Wisconsin, Madison on approximation algorithms for NP-hard optimization problems. We present integer programs for both GOPs that provide exact solutions. They showed that this problem is NP-hard even to approximate, and presented several heuristic algorithms. NP-complete problems are often addressed by using approximation algorithms. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. We would then do better by trying to design a good approximation algorithm rather than searching endlessly seeking an exact solution. Even if P is not equal to NP, there may be randomized algorithms (either Monte Carlo or Las Vegas) that can answer NP hard problems rapidly. There is an analogous notion of pathwidth which is also NP-complete. Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth. Approximating tree-width : Bodlaender et. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. Research Areas: Uses of randomness in complexity theory and algorithms; Efficient algorithms for finding approximate solutions to NP-hard problems (or proving that they don't exist); Cryptography. 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. Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. In this problem, multiple missions compete for sensor resources. We show both problems to be NP-hard and prove limits on approximation for both problems.