Divide-and-conquer approximation algorithms via spreading metrics

We present a novel divide-and-conquer paradigm for approximating NP-hard graph optimization problems. The paradigm models graph optimization problems that satisfy two properties: First, a divide-and-conquer approach is applicable. Second, a fractional spreading metric is computable in polynomial time. The spreading metric assigns fractional lengths to either edges or vertices of the input graph, such that all subgraphs on which the optimisation problem is non-trivial have large diameters. In addition, the spreading metric provides a lower bound, /spl tau/, on the cost of solving the optimization problem. We present a polynomial time approximation algorithm for problems modelled by our paradigm whose approximation factor is O (mi.