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Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems



Download Approximation Algorithms for NP-Hard Problems




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


Today is for its application to the field of hardness of approximation algorithms: It turns out that the PCP theorem is equivalent to saying that there are problems where computing even an approximate solution is NP-hard. Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. P & NP problems – NP complete problems- Approximation algorithms for NP hard problems- Traveling salesman problem – Knapsack problem. This paper deals with firefighter problem on rooted trees. SAT (boolean satisfiability, the "canonical" NP-hard problem) is a really tough nut to crack, whereas for example euclidean TSP (traveling salesman) is hard to solve optimally but has simple and fast algorithms that guarantee to solve it to within a constant factor of the optimum. It is known that the firefighter problem is NP-hard even for rooted trees of maximum degree 3. 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. A simple factor-2 approximation just walks around the spanning tree and can be computed in O(n log n) time with simple algorithms! We propose techniques to improve a given approximation algorithm. 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 . 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. What is a polynomial time algorithm? Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs.

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