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arXiv · 2609.07949

Improved Integrality Gap for Multicommodity Flow on Trees

Elfarouk Harb
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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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Elfarouk Harb. 2026-09-07. Improved Integrality Gap for Multicommodity Flow on Trees. https://arxiv.org/abs/2609.07949

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