PreprintarXiv licencearXiv
A Uniform Bound on Optimal Strategy Length in Water Transport Problem
Abstract
We prove that every water transport problem on an n-vertex graph has an optimal strategy of length at most n(2+o(1))n. More strongly, the convex hull of all strategy operators stabilizes within the same bound. We also give a five-vertex instance in which every optimal strategy repeats a nontrivial connected averaging set.
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BibTeX
@misc{tao2026uniform,
title = {{A Uniform Bound on Optimal Strategy Length in Water Transport Problem}},
author = {Tianyi Tao and Bohan Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30932},
eprint = {2609.30932},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30932},
}
RIS
TY - UNPB
TI - A Uniform Bound on Optimal Strategy Length in Water Transport Problem
AU - Tianyi Tao
AU - Bohan Yang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30932
UR - https://arxiv.org/abs/2609.30932
AB - We prove that every water transport problem on an n-vertex graph has an optimal strategy of length at most n^(2+o(1))n. More strongly, the convex hull of all strategy operators stabilizes within the same bound. We also give a five-vertex instance in which every optimal strategy repeats a nontrivial connected averaging set.
ER -