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Approximation Algorithms for NP-Hard Problems
Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

They showed that this problem is NP-hard even to approximate, and presented several heuristic algorithms. Note that hardness relations are always with respect to some reduction. 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. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. 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. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. Think too hard about approximation algorithms. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. Yet most such problems are NP-hard. The story goes something like this: say you're working as a software developer and your boss gives you this project so I give up,” you need to show your boss that it's NP-Hard and this motivates the studying of reductions. My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. Garey and Johnson, in 1978, list various possible ways to "cope" with NP-completeness, including looking for approximate algorithms and for algorithms that are efficient on average. Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. In this problem, multiple missions compete for sensor resources. We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. 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. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. 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. However, exact algorithms to solve the fractional MF problems have high computational complexity.

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