Don't Rock the Boat: Algorithms for Balanced Dynamic Loading and Unloading

We consider dynamic loading and unloading problems for heavy geometric objects. The challengeis to maintain balanced configurations at all times: minimize the maximal motion of the overall centerof gravity. While this problem has been studied from an algorithmic point of view, previous work onlyfocuses on balancing the final center of gravity; we give a variety of results for computing balancedloading and unloading schemes that minimize the maximal motion of the center of gravity duringthe entire process.In particular, we consider the one-dimensional case and distinguish between loading and unloading.In the unloading variant, the positions of the intervals are given, and we search for an optimalunloading order of the intervals. We prove that the unloading variant is NP-complete and give a2.7-approximation algorithm. In the loading variant, we have to compute both the positions ofthe intervals and their loading order. We give optimal approaches for several variants that modeldifferent loading scenarios that may arise, e.g., in the loading of a transport ship with containers.