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Approximation Algorithms for NP-Hard Problems epub

Approximation Algorithms for NP-Hard Problems. Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems

ISBN: 0534949681,9780534949686 | 620 pages | 16 Mb

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

In 2003 proved that it is still NP-hard and gave a polynomial-time algorithm with an approximation factor of 1nm. This paper deals with firefighter problem on rooted trees. 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. The problem is NP-hard and an approximation algorithm has been described in the reference. Yet most such problems are NP-hard. These results He helped create new approximation algorithms for fundamental optimization problems such as the Sparsest Cuts problem and the Euclidean Travelling Salesman problem, and contributed to the development of semi-definite programming as a practical algorithmic tool. I'm enjoying reading notes from Shuchi Chawla's course at the University of Wisconsin, Madison on approximation algorithms for NP-hard optimization problems. The Hitting Set problem is NP-hard [Karp' 72]. The reason the Cooper result holds is essentially that Bayes nets can be used to encode boolean satisfiability (SAT) problems, so solving the generic Bayes net inference problem lets you solve any SAT problem. Research Areas: Uses of randomness in complexity theory and algorithms; Efficient algorithms for finding approximate solutions to NP-hard problems (or proving that they don't exist); Cryptography. It is known that the firefighter problem is NP-hard even for rooted trees of maximum degree 3. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. Unfortunately the problem is not only NP-complete, but also hard to approximate. P & NP problems – NP complete problems- Approximation algorithms for NP hard problems- Traveling salesman problem – Knapsack problem. (So to solve an instance of the Hitting Set Problem, it suffices to solve the instance of your problem with. What is a polynomial time algorithm? No approximation algorithm with a ratio better than roughly 0.941 exists unless P=NP. Arora's research revolutionized the approach to essentially unsolvable problems that have long bedeviled the computing field, the so-called NP-complete problems. Thus unless P =NP, there are no efficient algorithms to find optimal solutions to such problems. We propose techniques to improve a given approximation algorithm.

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