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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

My answer is that is it ignores randomized and approximation algorithms. Approximating tree-width : Bodlaender et. 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. Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. Different approximation algorithms have their advantages and disadvantages. There is an analogous notion of pathwidth which is also NP-complete. Comparing Algorithms for the Traveling Salesman Problem. Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth. In 2003 proved that it is still NP-hard and gave a polynomial-time algorithm with an approximation factor of 1nm. The traveling salesman problem (TSP) is an NP-complete problem.