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

The Travelling-Salesman; Subset-Sum; Set-Covering. Unsurprisingly, submodular maximization tends to be NP-hard for most natural choices of constraints, so we look for approximation algorithms. Algorithms vis-à-vis Everyday Programming; Polynomial-Time Algorithms; NP-Complete Problems. It further motivates the study of approximation algorithms and other techniques to cope with NP-Completeness. The story goes something like this: say you're working as a software developer and your boss gives you this project so I give up,” you need to show your boss that it's NP-Hard and this motivates the studying of reductions. 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. Optimization/approximation algorithms/polynomial time/ NP-HARD. My algorithms professor used to tell his students (including me) this story to motivate studying NP-complete problems and reductions. We present integer programs for both GOPs that provide exact solutions. 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. Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. This book deals with designing polynomial time approximation algorithms for NP-hard optimization problems. We show both problems to be NP-hard and prove limits on approximation for both problems. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. Many combinatorial optimization problems can be expressed as the minimization or maximization of a submodular function, including min- and max-cut, coverage problems, and welfare maximization in algorithmic game theory. 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. We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. Approximation Algorithms for NP-Hard Problems pdf download.