Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

I'd started contemplating local optimizations, simulated annealing, etc. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. Think too hard about approximation algorithms. Problem classes P, NP, NP-hard and NP-complete, deterministic and non deterministic polynomial time algorithms., Approximation algorithms for some NP-complete problems. 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. Think about all the effort that's gone into finding approximation algorithms and hardness of approximation results for NP-complete problems. Unfortunately the problem is not only NP-complete, but also hard to approximate. No approximation algorithm with a ratio better than roughly 0.941 exists unless P=NP. I was expecting that I'd have to find an approximate solution, as this looked like a classic hairy NP-hard optimization problem. 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. My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. Yet most such problems are NP-hard.