Implementing approximation algorithms for the single-source unsplittable flow problem

In the single-source unsplittable flow problem, commodities must be routed simultaneously from a common source vertex to certain sinks in a given graph with edge capacities. The demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. This problem was introduced by Kleinberg [12] and generalizes several NP-complete problems. A cost value per unit of flow may also be defined for every edge. In this paper, we implement the 2-approximation algorithm of Dinitz, Garg, and Goemans [6] for congestion, which is the best known, and the (3,1)-approximation algorithm of Skutella [19] for congestion and cost, which is the best known bicriteria approximation. We study experimentally the quality of approximation achieved by the algorithms and the effect of heuristics on their performance. We also compare these algorithms against the previous best ones by Kolliopoulos and Stein [15].