Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and important numbers of commodities. We present and analyze in detail a heuristic based on the linear relaxation of the problem and randomized rounding. We provide empirical evidence that this approach is competitive with state-of-the-art resolution methods either by its scaling performance or by the quality of its solutions. We provide a variation of the heuristic which has the same approximation factor as the state-of-the-art approximation algorithm. We also derive a tighter analysis for the approximation factor of both the variation and the state-of-the-art algorithm. We introduce a new objective function for the unsplittable flow problem and discuss its differences with the classical congestion objective function. Finally, we discuss the gap in practical performance and theoretical guarantees between all the aforementioned algorithms.

翻译：不可分割流问题涵盖广泛的电信与运输问题，其高效求解对众多应用至关重要。本研究针对可扩展至大规模图结构和大量商品数量的算法展开探索。我们详细提出并分析了一种基于问题线性松弛与随机舍入的启发式算法。实验证据表明，该算法在扩展性能或解质量方面均能与当前最先进的求解方法相媲美。我们给出该启发式算法的一个变体，其近似比与最先进近似算法相同。同时，我们对该变体及最先进算法的近似比进行了更紧致的分析。针对不可分割流问题，我们引入了一个新的目标函数，并探讨其与传统拥塞目标函数的差异。最后，我们讨论了上述所有算法在实际性能与理论保证之间存在的差距。