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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

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

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. 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. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. Note that hardness relations are always with respect to some reduction. The field of "Sparse Approximation" deals with ways to perform atom decomposition, namely finding the atoms building the data vector. NP-complete problems are often addressed by using approximation algorithms. For graduate-level courses in approximation algorithms. When an NP-complete problem must be solved, one approach is to use a polynomial algorithm to approximate the solution; the answer thus obtained will not necessarily be optimal but will be reasonably close. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). Sanjeev Arora is one of the architects of the Probabilistically Checkable Proofs (PCP) theorem, which revolutionized our understanding of complexity and the approximability of NP-hard problems. It assumes familiarity with algorithms, mathematical proofs about the correctness of algorithms, probability theory and NP-completeness. 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. Rosea: This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. 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. The expected value of a discrete random variable). Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. 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. Due to the connection between approximation algorithms and computational optimization problems, reductions which preserve approximation in some respect are for this subject preferred than the usual Turing and Karp reductions. We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem.