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Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems



Approximation Algorithms for NP-Hard Problems epub




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


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. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. I'd started contemplating local optimizations, simulated annealing, etc. This book deals with designing polynomial time approximation algorithms for NP-hard optimization problems. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). Thus unless P =NP, there are no efficient algorithms to find optimal solutions to such problems. I was expecting that I'd have to find an approximate solution, as this looked like a classic hairy NP-hard optimization problem. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. Approximation Algorithms for NP-Hard Problems. With Christos Papadimitriou in 1988, he framed the systematic study of approximation algorithms for {mathsf{NP}} -hard optimization problems around the classes {mathsf{MaxNP}} and {mathsf{MaxSNP}} . When an NP-complete problem must be solved, one approach is to use a polynomial algorithm to approximate the solution; the answer thus obtained will not necessarily be optimal but will be reasonably close. Yet most such problems are NP-hard. However, exact algorithms to solve the fractional MF problems have high computational complexity. 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. In 2003 proved that it is still NP-hard and gave a polynomial-time algorithm with an approximation factor of 1nm. Numerous practical problems are integer optimization problems that are intractable.

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