{"paper":{"title":"No distributed quantum advantage for approximate graph coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.ET","quant-ph"],"primary_cat":"cs.DC","authors_text":"Augusto Modanese, Fabian Kuhn, Fran\\c{c}ois Le Gall, Francesco d'Amore, Gustav Schmid, Henrik Lievonen, Jukka Suomela, Marc-Olivier Renou, Rishikesh Gajjala, Xavier Coiteux-Roy","submitted_at":"2023-07-18T17:17:27Z","abstract_excerpt":"We give an almost complete characterization of the hardness of $c$-coloring $\\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit any distributed quantum advantage. To do that: 1) We give a new distributed algorithm that finds a $c$-coloring in $\\chi$-chromatic graphs in $\\tilde{\\mathcal{O}}(n^{\\frac{1}{\\alpha}})$ rounds, with $\\alpha = \\bigl\\lfloor\\frac{c-1}{\\chi - 1}\\bigr\\rfloor$. 2) We prove that any distributed algorithm for this problem requires $\\Omega(n^{\\frac{1}{\\alpha}})$ rounds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.09444","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.09444/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}