2026-08-05T19:04:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12561 2024-03-06T10:50:27Z ddc:004 open_access

Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut Bhangale, Amey Khot, Subhash Simultaneous CSPs Unique Games hardness Max-Cut A systematic study of simultaneous optimization of constraint satisfaction problems was initiated by Bhangale et al. [ICALP, 2015]. The simplest such problem is the simultaneous Max-Cut. Bhangale et al. [SODA, 2018] gave a .878-minimum approximation algorithm for simultaneous Max-Cut which is almost optimal assuming the Unique Games Conjecture (UGC). For single instance Max-Cut, Goemans-Williamson [JACM, 1995] gave an α_GW-approximation algorithm where α_GW ≈ .87856720... which is optimal assuming the UGC. It was left open whether one can achieve an α_GW-minimum approximation algorithm for simultaneous Max-Cut. We answer the question by showing that there exists an absolute constant ε₀ ≥ 10^{-5} such that it is NP-hard to get an (α_GW- ε₀)-minimum approximation for simultaneous Max-Cut assuming the Unique Games Conjecture. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Amey Bhangale and Subhash Khot 2020 Is Part Of LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2020.9 urn:nbn:de:0030-drops-125610 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.9 eng https://creativecommons.org/licenses/by/3.0/legalcode