Lecture 9 : Pipage Rounding Method
نویسنده
چکیده
In this lecture we study a different randomized rounding method called pipage rounding method. The materials of this lecture are based on the work of Chekuri, Vondrák and Zenklusen [CVZ10]. This method is stronger than the maximum entropy rounding by sampling method in some aspects and is weaker in some other aspects. From a highlevel point of view, one can use this method to round a fractional point in a matroid polytope to a basis in polynomial time making sure that the underlying elements of the matroid are negatively correlated. So, in particular, one can use this method to round a fractional point in the spanning tree polytope to a thin spanning tree similar to the idea in the last lecture. But as we will see in the next few lectures, the pipage rounding method does not necessarily satisfy several of the strong negative dependence properties that are satisfied by the maximum entropy distributions of spanning trees.
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