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

Yet most such problems are NP-hard. Presented at Computer Science Department, Sharif University of Technology (Optimization Seminar ). Think about all the effort that's gone into finding approximation algorithms and hardness of approximation results for NP-complete problems. Thus unless P =NP, there are no efficient algorithms to find optimal solutions to such problems. 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. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption. We then show that the selection of the optimal set of nodes for executing these modules is an NP-hard problem. Most of the problems I study are NP-hard so I focus mainly on approximation algorithms. In the Traveling Salesman is an NP-Hard problem. 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. 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. 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. Year of my PhD studies at the U of Alberta where I study the theory behind efficient algorithms for combinatorial optimization problems. Currently we have approximation algorithms that can come up with “good solutions” in a fairly acceptable amount of time. Problem classes P, NP, NP-hard and NP-complete, deterministic and non deterministic polynomial time algorithms., Approximation algorithms for some NP-complete problems. Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems.