Supersonic Overland Without a Sonic Boom: Quantitative Assessment of Mach-Cutoff Flight (Bernd Liebhardt, Florian Linke, and Martin Knaack)
Journal of Aircraft, 59(5):1257-1266, 2022.
@article{LiebhardtLinkeKnaack,
author = {Bernd Liebhardt and Florian Linke and Martin Knaack},
title = {Supersonic Overland Without a Sonic Boom: Quantitative Assessment of Mach-Cutoff Flight},
journal = {Journal of Aircraft},
volume = {59},
number = {5},
pages = {1257-1266},
year = {2022},
doi = {10.2514/1.C036637},
}
When flying at low supersonic speeds, rising temperatures and convenient winds can deflect the sonic boom shock waves so that they do not reach the ground. This work presents a computation methodology that incorporates atmospheric sonic ray tracing, topography, and realistic three-dimensional atmospheres in order to optimize supersonic overland cruise with respect to speed. Flight missions are simulated on several suitable city pairs using numerous atmospheric conditions. Flight times and fuel consumption are compared to subsonic high-speed missions.
Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint (Max Klimm and Martin Knaack)
APPROX 2022 – Proc. International Workshop on Approximation Algorithms for Combinatorial Optimization Problems.
@inproceedings{KlimmKnaack2022,
author = {Max Klimm and Martin Knaack},
title = {Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint},
booktitle = {APPROX 2022 – Proc. International Workshop on Approximation Algorithms for Combinatorial Optimization Problems},
year = {2022},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.49},
}
This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness factor of a policy is the worst case ratio of the solution obtained by following the policy and an optimal solution that knows the knapsack capacity. We develop an algorithm with a robustness factor that is decreasing in the curvature $c$ of the submodular function. For the extreme cases $c = 0$ corresponding to a modular objective, it matches a previously known and best possible robustness factor of $1/2$. For the other extreme case of $c = 1$ it yields a robustness factor of $\approx 0.35$ improving over the best previously known robustness factor of $\approx 0.06$.
