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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. There is an analogous notion of pathwidth which is also NP-complete. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. Approximating tree-width : Bodlaender et. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). Yet most such problems are NP-hard. Approximation Algorithm vs Heuristic. I'd started contemplating local optimizations, simulated annealing, etc. The reason the Cooper result holds is essentially that Bayes nets can be used to encode boolean satisfiability (SAT) problems, so solving the generic Bayes net inference problem lets you solve any SAT problem. This problem is known to be NP-hard even for alphabet of size 2. I was expecting that I'd have to find an approximate solution, as this looked like a classic hairy NP-hard optimization problem. Approximation algorithm: identifies approximate solutions to problems (mostly often NP-complete and NP-hard problems) to a certain bound. Product Description This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth.