Lecture 9 : Pipage Rounding Method

Lecture 6 & 7 : O ( log ( n ) / log log ( n ) ) Approximation Algorithms for ATSP

In the next few lectures we will talk about three new variants of the classical randomized rounding technique, namely the rounding by sampling method, the pipage rounding method and the iterative rounding method. We will use these techniques to design approximation algorithms for Asymmetric TSP (ATSP) and the Steiner tree problems. The materials of the this lecture are based on the works of Asa...

Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

On the Pipage Rounding Algorithm for Submodular Function Maximization - a View from Discrete Convex Analysis

We consider the problem of maximizing a nondecreasing submodular set function under a matroid constraint. Recently, Calinescu et al. (2007) proposed an elegant framework for the approximation of this problem, which is based on the pipage rounding technique by Ageev and Sviridenko (2004), and showed that this framework indeed yields a (1 − 1/e)-approximation algorithm for the class of submodular...

Dependent Rounding in Bipartite Graphs

We combine the pipage rounding technique of Ageev & Sviridenko witha recent rounding method developed by Srinivasan, to develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to the following applications: richer random-graph models for graphs with a given degree-s...

Pipage Rounding, Pessimistic Estimators and Matrix Concentration

Pipage rounding is a dependent random sampling technique that has several interesting properties and diverse applications. One property that has been particularly useful is negative correlation of the resulting vector. Unfortunately negative correlation has its limitations, and there are some further desirable properties that do not seem to follow from existing techniques. In particular, recent...