{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2019-02-13T12:59:33Z","oa_version":"Preprint","oa":1,"scopus_import":"1","publisher":"Society for Industrial & Applied Mathematics (SIAM)","status":"public","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"1193"}]},"quality_controlled":"1","title":"Commutativity in the algorithmic Lovász local lemma","day":"08","type":"journal_article","date_updated":"2023-09-19T14:24:58Z","month":"11","article_processing_charge":"No","issue":"6","publication_status":"published","date_published":"2018-11-08T00:00:00Z","abstract":[{"text":"We consider the recent formulation of the algorithmic Lov ́asz Local Lemma  [N. Har-vey and J. Vondr ́ak, inProceedings of FOCS, 2015, pp. 1327–1345; D. Achlioptas and F. Iliopoulos,inProceedings of SODA, 2016, pp. 2024–2038; D. Achlioptas, F. Iliopoulos, and V. Kolmogorov,ALocal Lemma for Focused Stochastic Algorithms, arXiv preprint, 2018] for finding objects that avoid“bad  features,”  or  “flaws.”   It  extends  the  Moser–Tardos  resampling  algorithm  [R.  A.  Moser  andG. Tardos,J. ACM, 57 (2010), 11] to more general discrete spaces.  At each step the method picks aflaw present in the current state and goes to a new state according to some prespecified probabilitydistribution (which depends on the current state and the selected flaw).  However, the recent formu-lation is less flexible than the Moser–Tardos method since it requires a specific flaw selection rule,whereas the algorithm of Moser and Tardos allows an arbitrary rule (and thus can potentially beimplemented more efficiently).  We formulate a new “commutativity” condition and prove that it issufficient for an arbitrary rule to work.  It also enables an efficient parallelization under an additionalassumption.  We then show that existing resampling oracles for perfect matchings and permutationsdo satisfy this condition.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1506.08547","open_access":"1"}],"department":[{"_id":"VlKo"}],"volume":47,"intvolume":"        47","year":"2018","isi":1,"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7"}],"author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov"}],"publication":"SIAM Journal on Computing","doi":"10.1137/16m1093306","page":"2029-2056","publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"external_id":{"arxiv":["1506.08547"],"isi":["000453785100001"]},"citation":{"mla":"Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovász Local Lemma.” <i>SIAM Journal on Computing</i>, vol. 47, no. 6, Society for Industrial &#38; Applied Mathematics (SIAM), 2018, pp. 2029–56, doi:<a href=\"https://doi.org/10.1137/16m1093306\">10.1137/16m1093306</a>.","ieee":"V. Kolmogorov, “Commutativity in the algorithmic Lovász local lemma,” <i>SIAM Journal on Computing</i>, vol. 47, no. 6. Society for Industrial &#38; Applied Mathematics (SIAM), pp. 2029–2056, 2018.","ama":"Kolmogorov V. Commutativity in the algorithmic Lovász local lemma. <i>SIAM Journal on Computing</i>. 2018;47(6):2029-2056. doi:<a href=\"https://doi.org/10.1137/16m1093306\">10.1137/16m1093306</a>","ista":"Kolmogorov V. 2018. Commutativity in the algorithmic Lovász local lemma. SIAM Journal on Computing. 47(6), 2029–2056.","chicago":"Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovász Local Lemma.” <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics (SIAM), 2018. <a href=\"https://doi.org/10.1137/16m1093306\">https://doi.org/10.1137/16m1093306</a>.","apa":"Kolmogorov, V. (2018). Commutativity in the algorithmic Lovász local lemma. <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics (SIAM). <a href=\"https://doi.org/10.1137/16m1093306\">https://doi.org/10.1137/16m1093306</a>","short":"V. Kolmogorov, SIAM Journal on Computing 47 (2018) 2029–2056."},"ec_funded":1,"_id":"5975","language":[{"iso":"eng"}]}