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arXiv · 2611.06957

An Integrality-Gap Lower Bound of 1.2325 for Minimum Multiway Cut

Dimitar Chakarov·Yury Makarychev
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Abstract

We prove that the integrality gap of the Călinescu-Karloff-Rabani relaxation for Minimum Multiway Cut is at least $1.2325$ when the number of terminals is large. By a result of Manokaran, Naor, Raghavendra, and Schwartz (2008), it is therefore NP-hard, under the Unique Games Conjecture, to approximate Minimum Multiway Cut within a factor of $1.2325$. This improves the previously best known lower bound of $1.20016$ due to Bérczi, Chandrasekaran, Király, and Madan (2020).

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Dimitar Chakarov, Yury Makarychev. 2026-11-03. An Integrality-Gap Lower Bound of 1.2325 for Minimum Multiway Cut. https://arxiv.org/abs/2611.06957

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