Rounding in -approximation algorithms

Approximation Algorithms: LP Relaxation, Rounding, and Randomized Rounding Techniques

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...

Rounding Techniques for Semidefinite Relaxations

This report reviews some approximation algorithms for combinatorial optimization problems, based on a semidefinite relaxation followed by randomized rounding.

Approximation algorithms via randomized rounding: a survey

Approximation algorithms provide a natural way to approach computationally hard problems. There are currently many known paradigms in this area, including greedy algorithms, primal-dual methods, methods based on mathematical programming (linear and semidefinite programming in particular), local improvement, and “low distortion” embeddings of general metric spaces into special families of metric...

A Randomized Rounding Algorithm for the Asymmetric Traveling Salesman Problem

We present an algorithm for the asymmetric traveling salesman problem on instances which satisfy the triangle inequality. Like several existing algorithms, it achieves approximation ratio O(log n). Unlike previous algorithms, it uses randomized rounding.