A New Approximation Technique for Resource-Allocation Problems

TL;DR

This paper introduces a novel rounding technique using random walks in polytopes, enhancing approximation algorithms and integrality gaps for resource allocation and scheduling problems, including generalized assignment with job dropping.

Contribution

It generalizes previous work on assignment problems by incorporating job dropping and develops new concentration bounds for bipartite matching.

Findings

Improved approximation algorithms for resource allocation problems.

Enhanced integrality gap bounds for generalized assignment.

New concentration bounds for random bipartite matching.

Abstract

We develop a rounding method based on random walks in polytopes, which leads to improved approximation algorithms and integrality gaps for several assignment problems that arise in resource allocation and scheduling. In particular, it generalizes the work of Shmoys and Tardos on the generalized assignment problem to the setting where some jobs can be dropped. New concentration bounds for random bipartite matching are developed as well.