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

It assumes familiarity with algorithms, mathematical proofs about the correctness of algorithms, probability theory and NP-completeness. Explain NP-Complete and NP- Hard problem. Approximation algorithm: identifies approximate solutions to problems (mostly often NP-complete and NP-hard problems) to a certain bound. Approximation Algorithm vs Heuristic. The expected value of a discrete random variable). For graduate-level courses in approximation algorithms. TOP 30 IMPORTANT QUESTION OF Design & Analysis of Algorithm(DAA) For GBTU/MMTU C.S./I.T. 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. Unfortunately the problem is not only NP-complete, but also hard to approximate. 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. Also Discuss What is meant by P(n)-approximation algorithm? Numerous practical problems are integer optimization problems that are intractable. Finally, we assume that the reader knows something about NP-completeness, at least enough to know that there might be good reason for wanting fast, approximate solutions to NP-hard discrete optimization problems. No approximation algorithm with a ratio better than roughly 0.941 exists unless P=NP. Approximation Algorithms for NP-Hard Problems. A simple factor-2 approximation just walks around the spanning tree and can be computed in O(n log n) time with simple algorithms!