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

Linear programming has been a successful tool in combinatorial optimization to achieve polynomial time algorithms for problems in P and also to achieve good approximation algorithms for problems which are NP-hard. 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. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). The fractional MF problems are polynomial time solvable while integer versions are NP-complete. I'm enjoying reading notes from Shuchi Chawla's course at the University of Wisconsin, Madison on approximation algorithms for NP-hard optimization problems. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. However, exact algorithms to solve the fractional MF problems have high computational complexity. Have you ever wondered if a specific NP-hard problem has an approximation algorithm or not? Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. Yet most such problems are NP-hard. The problem is NP hard for all non-trivial values of k and d and there are various approximation algorithms for solving this problem. If yes, you may like to visit this site: A Compendium of NP optimization problems. I also wanted to include just a little bit of my own opinion on why studying approximation algorithms is worthwhile.