Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum
Approximation Algorithms for NP-Hard Problems Dorit Hochbaum ebook
ISBN: 0534949681, 9780534949686
Publisher: Course Technology
Because all of these problems are NP-hard, the primary goal of this research is to produce polynomial-time, approximation algorithms for each problem considered. In the Traveling Salesman is an NP-Hard problem. Instead of trying to solve this problem exactly, we will reason about whether constant factor approximation algorithms exist, i.e. 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. In this problem, multiple missions compete for sensor resources. Moreover, we prove that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms. Currently we have approximation algorithms that can come up with “good solutions” in a fairly acceptable amount of time. (So to solve an instance of the Hitting Set Problem, it suffices to solve the instance of your problem with. Have you ever wondered if a specific NP-hard problem has an approximation algorithm or not? They showed that this problem is NP-hard even to approximate, and presented several heuristic algorithms. If one can establish a problem as NP-complete, there is strong reason to believe that it is intractable. It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). If yes, you may like to visit this site: A Compendium of NP optimization problems. We would then do better by trying to design a good approximation algorithm rather than searching endlessly seeking an exact solution. This is one of Karp's original NP-complete problems. The Hitting Set problem is NP-hard [Karp' 72].
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