Experimental Evaluation of Approximation Algorithms for Single-Source Unsplittable Flow

Abstract

In the single-source unsplittable flow problem, we are given a network G, a source vertex s and k commodities with sinks ti and real-valued demands ρi, 1 ≤ i ≤ k. We seek to route the demand ρi of each commodity i along a single s-ti flow path, so that the total flow routed across any edge e is bounded by the edge capacity ce. This NP-hard problem combines the difficulty of bin-packing with routing through an arbitrary graph and has many interesting and important variations. In this paper we initiate the experimental evaluation of approximation algorithms for unsplittable flow problems. We examine the quality of approximation achieved by several algorithms for finding a solution with near-optimal congestion. In the process we analyze theoretically a new algorithm and report on the practical relevance of heuristics based on minimum-cost flow. The experimental results demonstrate practical performance that is better than the theoretical guarantees for all algorithms tested. Moreover modifications to the algorithms to achieve better theoretical results translate to improvements in practice as well.