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.

This study investigates the performance of an innovative routing protocol inspired by the Unsplittable Multi-Commodity Flow (UMCF) problem. LEO routing schemes are often based on Shortest Path (SP) algorithms, the Floyd-Warshall algorithm is usually chosen to compute these network paths within the constellation and their end-toend latency. Instead of considering latency as a criterion, we seek to optimize the overall amount of IP traffic crossing the constellation. This criterion can be optimized by considering the Unsplittable Multi Commodity Flow problem associated with the system. To solve this problem, we use a heuristic algorithm based on randomized rounding that was shown to return solutions of good quality of the Unsplittable Multi Commodity Flow problem in the optimization literature. Using network simulation over Telesat constellation, we show this proposal significantly reduces the overall congestion level compared to the standard SP routing schemes.

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