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.

不可分割流问题涵盖了广泛的电信和运输问题，其有效解决是许多应用的关键。在这项工作中，我们研究了可以扩展到大型图形和重要数量商品的算法。我们提出并详细分析了基于问题的线性松弛和随机舍入的启发式方法。我们提供的经验证据表明，这种方法无论是在扩展性能还是解决方案的质量方面都可以与最先进的解决方法相媲美。我们提供了启发式的变体，它具有与最先进的近似算法相同的近似因子。我们还对变化和最先进算法的近似因子进行了更严格的分析。我们为不可分割流问题引入了一种新的目标函数，并讨论了它与经典拥塞目标函数的区别。最后，我们讨论所有上述算法在实际性能和理论保证方面的差距。