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

Approximation Algorithms for NP-Hard Problems. Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems

ISBN: 0534949681,9780534949686 | 620 pages | 16 Mb

Download Approximation Algorithms for NP-Hard Problems

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

Study of low-distortion embeddings (which can be pursued in a more general setting) has been a highly-active TCS research topic, largely due to its role in designing efficient approximation algorithms for NP-hard problems. 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. It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. A simple factor-2 approximation just walks around the spanning tree and can be computed in O(n log n) time with simple algorithms! Approximation Algorithm vs Heuristic. For these problems, approximation algorithms are good choices. Here is an example to give a feeling. Approximation algorithm: identifies approximate solutions to problems (mostly often NP-complete and NP-hard problems) to a certain bound. As we know, NP-hard problems are nightmare for the computers. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. 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.

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