Safe Approximation—An Efficient Solution for a Hard Routing Problem

The Disjoint Connecting Paths problem and its capacitated generalization, called Unsplittable Flow problem, play an important role in practical applications such as communication network design routing. These tasks are NP-hard general, but various polynomial-time approximations known. Nevertheless, the tend to be either too loose (allowing large deviation from optimum), or complicated, often rendering them impractical large, complex networks. Therefore, our goal is present a solution that provides relatively simple, efficient algorithm for unsplittable flow directed graphs, where task NP-hard, known remain even approximate up factor. efficiency of achieved by sacrificing small part space. This also represents novel paradigm approximation. Rather than giving search exact solution, we restrict space subset most applications, excludes only marginal some well-defined sense. Specifically, sacrificed contains scenarios edges very close saturation. Since nearly saturated links undesirable therefore, excluding near saturation quite reasonable point view. We refer solutions contain no safe solutions, call approach prove this approximation can carried out efficiently. That is, once ourselves find optimum randomized polynomial time algorithm.