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arXiv:2611.06957 · v1

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

Dimitar ChakarovYury Makarychev
cs.DS
首次提交 2026-11-04 06:49
版本更新 2026-11-04 06:49
雷达观测 2026-11-06 10:05
arXiv ↗PDF ↗

摘要

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).

作者备注：37 pages, 2 figures

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v1 · 2026-11-04 06:49 · 最新观测版本

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

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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