Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

Approximation Algorithm for NP-hard problems by Dorit Hochbaum is a set of chapters by different contributors. There are already arbitrarily good polynomial-time approximation algorithms for many NPO-complete problems like TSP, but TSP is actually APX-complete too, meaning you cannot even approximate answers beyond a certain factor unless P=NP. The problem is NP-hard and an approximation algorithm has been described in the reference. There is an analogous notion of pathwidth which is also NP-complete. Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. Approximating tree-width : Bodlaender et. I still maintain that someone could make a good movie with the premise "random guy finds easy algorithm to solve NP-complete problems now what?" in the vein of Primer (random guys . 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. It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). Perhaps, the best source on approximation algorithms. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. I also wanted to include just a little bit of my own opinion on why studying approximation algorithms is worthwhile. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth. To minimum spanning trees and Huffman codes; dynamic programming, including applications to sequence alignment and shortest-path problems; and exact and approximate algorithms for NP-complete problems. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ).