{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"D.G. Harris, F. Iliopoulos, V. Kolmogorov, Theory of Computing 21 (2025) 1–34.","ama":"Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the algorithmic Lovász Local Lemma. <i>Theory of Computing</i>. 2025;21(5):1-34. doi:<a href=\"https://doi.org/10.4086/toc.2025.v021a005\">10.4086/toc.2025.v021a005</a>","ieee":"D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity for the algorithmic Lovász Local Lemma,” <i>Theory of Computing</i>, vol. 21, no. 5. University of Chicago Press, pp. 1–34, 2025.","ista":"Harris DG, Iliopoulos F, Kolmogorov V. 2025. A new notion of commutativity for the algorithmic Lovász Local Lemma. Theory of Computing. 21(5), 1–34.","chicago":"Harris, David G., Fotios Iliopoulos, and Vladimir Kolmogorov. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” <i>Theory of Computing</i>. University of Chicago Press, 2025. <a href=\"https://doi.org/10.4086/toc.2025.v021a005\">https://doi.org/10.4086/toc.2025.v021a005</a>.","mla":"Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” <i>Theory of Computing</i>, vol. 21, no. 5, University of Chicago Press, 2025, pp. 1–34, doi:<a href=\"https://doi.org/10.4086/toc.2025.v021a005\">10.4086/toc.2025.v021a005</a>.","apa":"Harris, D. G., Iliopoulos, F., &#38; Kolmogorov, V. (2025). A new notion of commutativity for the algorithmic Lovász Local Lemma. <i>Theory of Computing</i>. University of Chicago Press. <a href=\"https://doi.org/10.4086/toc.2025.v021a005\">https://doi.org/10.4086/toc.2025.v021a005</a>"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"08","date_updated":"2026-02-10T10:00:00Z","intvolume":"        21","license":"https://creativecommons.org/licenses/by/4.0/","_id":"21143","ec_funded":1,"year":"2025","article_type":"original","acknowledgement":"This material is based on work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the National Science Foundation Grant No. CCF-1815328. Supported by the European Research Council under the European Union’s Seventh Framework Programme\r\n(FP7/2007-2013)/ERC grant agreement no 616160.","volume":21,"month":"09","issue":"5","has_accepted_license":"1","oa_version":"Published Version","quality_controlled":"1","doi":"10.4086/toc.2025.v021a005","type":"journal_article","date_published":"2025-09-08T00:00:00Z","abstract":[{"text":"The Lovász Local Lemma (LLL) is a powerful tool in probabilistic\r\ncombinatorics which can be used to establish the existence of objects with certain\r\nproperties. The breakthrough paper by Moser & Tardos (STOC’09 and JACM 2010)\r\nand follow-up work revealed that the LLL has intimate connections with a class of\r\nstochastic local search algorithms for finding such desirable objects.\r\nBesides conditions for convergence, many other natural questions can be asked\r\nabout algorithms; for instance, “are they parallelizable?”, “how many solutions can\r\nthey output?”, “what is the expected ‘weight’ of a solution?”. These questions and\r\nmore have been answered for a class of LLL-inspired algorithms called commutative. In\r\nthis paper we introduce a new, very natural and more general notion of commutativity\r\n(essentially matrix commutativity) which allows us to show a number of new refined\r\nproperties of LLL-inspired local search algorithms with significantly simpler proofs.","lang":"eng"}],"publisher":"University of Chicago Press","OA_type":"diamond","ddc":["510"],"publication_status":"published","department":[{"_id":"VlKo"}],"publication_identifier":{"eissn":["1557-2862"]},"oa":1,"file_date_updated":"2026-02-10T09:54:28Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10072"}]},"author":[{"last_name":"Harris","full_name":"Harris, David G.","first_name":"David G."},{"full_name":"Iliopoulos, Fotios","last_name":"Iliopoulos","first_name":"Fotios"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"}],"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7"}],"file":[{"date_created":"2026-02-10T09:54:28Z","relation":"main_file","file_name":"2025_TheoryComputing_Harris.pdf","file_id":"21209","access_level":"open_access","file_size":509346,"content_type":"application/pdf","checksum":"5a9f7cfccac6046fe75a14a4059eed04","success":1,"date_updated":"2026-02-10T09:54:28Z","creator":"dernst"}],"external_id":{"arxiv":["2008.05569"]},"language":[{"iso":"eng"}],"corr_author":"1","PlanS_conform":"1","arxiv":1,"OA_place":"publisher","page":"1 - 34","date_created":"2026-02-05T12:04:58Z","article_processing_charge":"No","status":"public","publication":"Theory of Computing","title":"A new notion of commutativity for the algorithmic Lovász Local Lemma"}