New algorithms for the minimum-cost single-source unsplittable flow problem

The Minimum-Cost Single-Source Unsplittable Flow problem is a Single-Source multi-commodity flow problem in which each commodity should be shipped only on one single path at the minimum possible cost without violating the capacity of each edge. An outstanding open question on this problem is whether a simultaneous (2,1)-approximation can be achieved for minimizing congestion and cost. But for the general version so far the best possible ratio is (3 + 2√2, 1). In this paper we present a polynomial-time approximation algorithms which achieves this approximation ratio, our algorithm is more efficient and easier to implement compares to previous algorithms for this problem.