@article{Akitaya_Biniaz_Bose_De Carufel_Maheshwari_da Silveira_Smid_2023, title={The Minimum Moving Spanning Tree Problem}, volume={27}, url={https://jgaa.info/index.php/jgaa/article/view/paper607}, DOI={10.7155/jgaa.00607}, abstractNote={We investigate the problem of finding a spanning tree of a set of $n$ moving points in $\mathbb{R}^{\dim}$ that minimizes the maximum total weight (under any convex distance function) or the maximum bottleneck throughout the motion.
The output is a single tree, i.e., it does not change combinatorially during the movement of the points.
We call these trees a minimum moving spanning tree, and a minimum bottleneck moving spanning tree, respectively.
We show that, although finding the minimum bottleneck moving spanning tree can be done in $O(n^2)$ time when $\dim$ is a constant, it is NP-hard to compute the minimum moving spanning tree even for $\dim=2$.
We provide a simple $O(n^2)$-time 2-approximation and a $O(n \log n)$-time $(2+\varepsilon)$-approximation for the latter problem, for any constant $\dim$ and any constant $\varepsilon>0$.}, number={1}, journal={Journal of Graph Algorithms and Applications}, author={Akitaya, Hugo and Biniaz, Ahmad and Bose, Prosenjit and De Carufel, Jean-Lou and Maheshwari, Anil and da Silveira, Luís Fernando Schultz Xavier and Smid, Michiel}, year={2023}, month={Jan.}, pages={1–18} }