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

TL;DR

This paper studies algorithms for dynamically loading and unloading heavy objects while maintaining a balanced center of gravity, introducing new approaches for both loading and unloading scenarios with theoretical and practical implications.

Contribution

It provides the first comprehensive analysis of balanced dynamic loading and unloading, including NP-completeness results and approximation algorithms for the unloading case, and optimal solutions for various loading scenarios.

Findings

Unloading variant is NP-complete.

A 2.7-approximation algorithm for unloading.

Optimal algorithms for several loading scenarios.

Abstract

We consider dynamic loading and unloading problems for heavy geometric objects. The challenge is to maintain balanced configurations at all times: minimize the maximal motion of the overall center of gravity. While this problem has been studied from an algorithmic point of view, previous work only focuses on balancing the final center of gravity; we give a variety of results for computing balanced loading and unloading schemes that minimize the maximal motion of the center of gravity during the 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 optimal unloading order of the intervals. We prove that the unloading variant is NP-complete and give a 2.7-approximation algorithm. In the loading variant, we have to compute both the positions of the intervals and their loading order. We give optimal approaches for several variants that model different loading scenarios that may arise, e.g., in the loading of a transport ship with containers.