Approximation via cost sharing

We present constant-factor approximation algorithms for several widely-studied NP-hard optimization problems in network design, including the multicommodity rent-or-buy, virtual private network design, and single-sink buy-at-bulk problems. Our algorithms are simple and their approximation ratios improve over those previously known, in some cases by orders of magnitude. We develop a general analysis framework to bound the approximation ratios of our algorithms. This framework is based on a novel connection between random sampling and game-theoretic cost sharing.