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

Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. 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 Travelling-Salesman; Subset-Sum; Set-Covering. The problem is NP hard for all non-trivial values of k and d and there are various approximation algorithms for solving this problem. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. Algorithms vis-à-vis Everyday Programming; Polynomial-Time Algorithms; NP-Complete Problems. However, exact algorithms to solve the fractional MF problems have high computational complexity. Yet most such problems are NP-hard. Many of the striking advances in theoretical computer science over the past two decades concern approximation algorithms, which compute provably near-optimal solutions to NP-hard optimization problems. To minimum spanning trees and Huffman codes; dynamic programming, including applications to sequence alignment and shortest-path problems; and exact and approximate algorithms for NP-complete problems. Optimization/approximation algorithms/polynomial time/ NP-HARD. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. 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.