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

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. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions 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. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. NP, in the worst case, no polynomial-time algorithm guarantees a cover of cost [Math Processing Error] [2]. (This blog is about how to use randomized rounding to systematically derive greedy approximation algorithms and Lagrangian-relaxation algorithms. Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth. Here is a review of the Set Cover problem and the classic greedy algorithm for it. Equations are not displayed properly. We then show that the selection of the optimal set of nodes for executing these modules 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. Note that hardness relations are always with respect to some reduction. Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. Problem definition; Greedy algorithm; Remarks; Related; Bibliography. Approximating tree-width : Bodlaender et. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. There is an analogous notion of pathwidth which is also NP-complete. I normally do machine learning work, and when I'm evaluating an algorithm on a data set, I always use cross-validation to determine how effective the. Combining theories of hypothesis testing, stochastic analysis, and approximation algorithms, we develop a framework to counter different threats while minimizing the resource consumption.