Approximation Algorithms for NP-Hard Problems

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

For these problems, approximation algorithms are good choices. Algorithms vis-ŕ-vis Everyday Programming; Polynomial-Time Algorithms; NP-Complete Problems. The Travelling-Salesman; Subset-Sum; Set-Covering. As we know, NP-hard problems are nightmare for the computers. The computer scientist Richard Karp, of the University of California at Berkeley, showed that the traveling salesman problem is “NP-hard,” which means that it has no efficient algorithm (unless a famous conjecture called P=NP is true — but the majority of computer scientists now suspect that it is false). € traveling salesperson problem, Steiner tree. A less obvious application is that the minimum spanning tree can be used to approximately solve the traveling salesman problem. Approximation algorithms for NP-hard problems. This problem is known to be NP-hard even for alphabet of size 2. The problem is NP hard for all non-trivial values of k and d and there are various approximation algorithms for solving this problem. My answer is that is it ignores randomized and approximation algorithms. An infinitesimal advance in the traveling salesman problem breathes new life into the search for improved approximate solutions. The study of approximation algorithms for NP-hard problems has blossomed into a rich field, especially as a result of intense work over the last two decades. Here is an example to give a feeling. 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. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential.