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

With Christos Papadimitriou in 1988, he framed the systematic study of approximation algorithms for {mathsf{NP}} -hard optimization problems around the classes {mathsf{MaxNP}} and {mathsf{MaxSNP}} . It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). For graduate-level courses in approximation algorithms. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. The expected value of a discrete random variable). We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. Linear programming has been a successful tool in combinatorial optimization to achieve polynomial time algorithms for problems in P and also to achieve good approximation algorithms for problems which are NP-hard. It assumes familiarity with algorithms, mathematical proofs about the correctness of algorithms, probability theory and NP-completeness. We obtain computationally simple optimal rules for aggregating and thereby minimizing the errors in the decisions of the nodes executing the intrusion detection software (IDS) modules. Finally, we assume that the reader knows something about NP-completeness, at least enough to know that there might be good reason for wanting fast, approximate solutions to NP-hard discrete optimization problems.