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Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for NP-Hard Problems. Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems


Approximation.Algorithms.for.NP.Hard.Problems.pdf
ISBN: 0534949681,9780534949686 | 620 pages | 16 Mb


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




We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. We obtain computationally simple optimal rules for aggregating and thereby minimizing the errors in the decisions of the nodes executing the intrusion detection software (IDS) modules. Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. Moreover, we prove that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms. There is an analogous notion of pathwidth which is also NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. My answer is that is it ignores randomized and approximation algorithms. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. Rosea: This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. Approximating tree-width : Bodlaender et. This is one of Karp's original NP-complete problems. Instead of trying to solve this problem exactly, we will reason about whether constant factor approximation algorithms exist, i.e. 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. Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth.

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