PreprintCC BY 4.0arXiv
Improved Integrality Gap for Multicommodity Flow on Trees
Abstract
We improve the best known lower bound on the integrality gap for weighted unit-demand multicommodity flow on trees from 1/4 to 2/5, improving on the long-standing bound of Chekuri, Mydlarz, and Shepherd~\cite{CMS}. We give the proof in two stages. First, a surprisingly simple packing lemma and an inductive coloring argument give an intermediate bound of 4/11. We then refine the argument to obtain 2/5.
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BibTeX
@misc{harb2026improved,
title = {{Improved Integrality Gap for Multicommodity Flow on Trees}},
author = {Elfarouk Harb},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07949},
eprint = {2609.07949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07949},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved Integrality Gap for Multicommodity Flow on Trees
AU - Elfarouk Harb
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07949
UR - https://arxiv.org/abs/2609.07949
AB - We improve the best known lower bound on the integrality gap for weighted unit-demand multicommodity flow on trees from 1/4 to 2/5, improving on the long-standing bound of Chekuri, Mydlarz, and Shepherd~\cite{CMS}. We give the proof in two stages. First, a surprisingly simple packing lemma and an inductive coloring argument give an intermediate bound of 4/11. We then refine the argument to obtain 2/5.
ER -