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.

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The aircraft scheduling problem consists in sequencing aircraft on airport runways and in scheduling their times of operations taking into consideration several operational constraints. It is known to be an NP-hard problem, an ongoing challenge for both researchers and air traffic controllers.The aim of this paper is to present a focused review on the most relevant techniques in the recent literature (since 2010) on the aircraft runway scheduling problem, including exact approaches such as mixed-integer programming and dynamic programming, metaheuristics, and novel approaches based on reinforcement learning. Since the benchmark instances used in the literature are easily solved by high-performance computers and current versions of solvers, we propose a new data set with challenging realistic problems constructed from real-world air traffic.

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