Lecture 16: Approximation Algorithms
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Lec . 2 : Approximation Algorithms for NP - hard Problems ( Part II )
We will continue the survey of approximation algorithms in this lecture. First, we will discuss a (1+ε)-approximation algorithm for Knapsack in time poly(n, 1/ε). We will then see applications of some heavy hammers such as linear programming (LP) and semi-definite programming (SDP) towards approximation algorithms. More specifically, we will see LPbased approximation for MAXSAT and MAXCUT. In t...
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In lecture 19, we saw an LP relaxation based algorithm to solve the sparsest cut problem with an approximation guarantee of O(logn). In this lecture, we will show that the integrality gap of the LP relaxation is O(logn) and hence this is the best approximation factor one can get via the LP relaxation. We will also start developing an SDP relaxation based algorithm which provides an O( √ log n) ...
متن کاملApproximation Algorithms and Hardness of Approximation March 19 , 2013 Lecture 9 and 10 : Iterative rounding II
In the last lecture we saw a framework for building approximation algorithms using iterative rounding: 1. Formulate the problem as a linear program (LP) 2. Characterise extreme point structure 3. Iterative algorithm 4. Analysis We used this framework to solve two problems: Matchings in Bipartite Graphs and the Generalised Assignment Problem. A negative point about this approach is that it requi...
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تاریخ انتشار 2008