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

The traveling salesman problem (TSP) is an NP-complete problem. As we know, NP-hard problems are nightmare for the computers. For these problems, approximation algorithms are good choices. Garey and Johnson, in 1978, list various possible ways to "cope" with NP-completeness, including looking for approximate algorithms and for algorithms that are efficient on average. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. Even if P is not equal to NP, there may be randomized algorithms (either Monte Carlo or Las Vegas) that can answer NP hard problems rapidly. My answer is that is it ignores randomized and approximation algorithms. Comparing Algorithms for the Traveling Salesman Problem. Different approximation algorithms have their advantages and disadvantages. Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. However, exact algorithms to solve the fractional MF problems have high computational complexity. Here is an example to give a feeling.