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

(So to solve an instance of the Hitting Set Problem, it suffices to solve the instance of your problem with. Think about all the effort that's gone into finding approximation algorithms and hardness of approximation results for NP-complete problems. Study of low-distortion embeddings (which can be pursued in a more general setting) has been a highly-active TCS research topic, largely due to its role in designing efficient approximation algorithms for NP-hard problems. Product Description This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. This problem addresses the issue of timing when deploying viral campaigns. We present integer programs for both GOPs that provide exact solutions. If one can establish a problem as NP-complete, there is strong reason to believe that it is intractable. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. They showed that this problem is NP-hard even to approximate, and presented several heuristic algorithms. We would then do better by trying to design a good approximation algorithm rather than searching endlessly seeking an exact solution. The Hitting Set problem is NP-hard [Karp' 72]. We show both problems to be NP-hard and prove limits on approximation for both problems. Both these problems are NP-hard, which motivates our interest in their approximation. In this problem, multiple missions compete for sensor resources. In spite of their theoretical hardness, heuristic solvers are often able to solve large realistic problem instances surprisingly fast.