{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:24:46Z","timestamp":1787239486404,"version":"build-2736575974"},"reference-count":176,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100002790","name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN-2019-04067, DGECR-2019-00147"],"award-info":[{"award-number":["RGPIN-2019-04067, DGECR-2019-00147"]}],"id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008297","name":"Cray Incorporated","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008297","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000185","name":"Defense Advanced Research Projects Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100002418","name":"Intel Corporation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100002418","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000104","name":"National Aeronautics and Space Administration","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000104","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1546488"],"award-info":[{"award-number":["IIS-1546488"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1909528"],"award-info":[{"award-number":["CCF-1909528"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-0939370"],"award-info":[{"award-number":["CCF-0939370"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0014543"],"award-info":[{"award-number":["DE-SC0014543"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p>Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to \u201crefine\u201d or \u201cimprove\u201d a given cluster that has been obtained by some other method. In this survey, we focus on principled algorithms for this cluster improvement problem. Many such cluster improvement algorithms are flow-based methods, by which we mean that operationally they require the solution of a sequence of maximum flow problems on a (typically implicitly) modified data graph. These cluster improvement algorithms are powerful, both in theory and in practice, but they have not been widely adopted for problems such as community detection, local graph clustering, semisupervised learning, etc. Possible reasons for this are the steep learning curve for these algorithms, the lack of efficient and easy-to-use software, and the lack of detailed numerical experiments on real-world data that demonstrate their usefulness. Our objective here is to address these issues. To do so, we guide the reader through the whole process of understanding how to implement and apply these powerful algorithms. We present a unifying fractional programming optimization framework that permits us to distill, in a simple way, the crucial components of all these algorithms. This also makes apparent similarities and differences among related methods. Viewing these cluster improvement algorithms via a fractional programming framework suggests directions for future algorithm development. Finally, we develop efficient implementations of these algorithms in our LocalGraphClustering Python package, and we perform extensive numerical experiments to demonstrate the performance of these methods on social networks and image-based data graphs.<\/jats:p>","DOI":"10.1137\/20m1333055","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T12:38:38Z","timestamp":1675946318000},"page":"59-143","source":"Crossref","is-referenced-by-count":4,"title":["Flow-Based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance"],"prefix":"10.1137","volume":"65","author":[{"given":"Kimon","family":"Fountoulakis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1619-3797","authenticated-orcid":true,"given":"Meng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8107-6474","authenticated-orcid":true,"given":"David F.","family":"Gleich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael W.","family":"Mahoney","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"atypb1","author":"Abbe E.","year":"2018","journal-title":"J. Mach. Learn. Res., 18, art. 177, http:\/\/jmlr.org\/papers\/v18\/16-480.html."},{"key":"atypb2","first-page":"121","volume-title":"Advances in Neural Information Processing Systems 21","author":"Ackerman M.","year":"2018"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2006.44"},{"key":"atypb4","author":"Andersen R.","year":"2016","journal-title":"J. ACM, 63, art. 15."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1145\/1135777.1135814"},{"key":"atypb6","first-page":"651","volume-title":"Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms","author":"Andersen R.","year":"2008"},{"key":"atypb7","author":"Arora S.","year":"2009","journal-title":"J. ACM, 56 (2), art. 5."},{"key":"atypb8","first-page":"1795","volume-title":"Proceedings of the 32nd International Conference on Machine Learning, PMLR","author":"Avron H.","year":"2015"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1145\/2688073.2688116"},{"key":"atypb10","volume-title":"Python-Louvain, https:\/\/github.com\/taynaud\/python-louvain","author":"Aynaud T.","year":"2018"},{"key":"atypb11","first-page":"2399","volume":"7","author":"Belkin M.","year":"2006","journal-title":"J. Mach. Learn. Res."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v32i1.12221"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1126\/science.aad9029"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/16M1070426"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/130910312"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2008\/10\/P10008"},{"key":"atypb17","first-page":"19","volume-title":"Proceedings of the Eighteenth International Conference on Machine Learning, Morgan Kaufmann","author":"Blum A.","year":"2001"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-006-7934-5"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2004.60"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-28831-7_5"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/b106453"},{"key":"atypb23","volume-title":"Genome Biology, 7, art. R8.","author":"Brown S. D.","year":"2006"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.862083"},{"key":"atypb25","first-page":"72","volume-title":"Proceedings of the Workshop on Clustering Large Data Sets at the 2003 International Conference on Data Mining","author":"Carrasco J. J.","year":"2003"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/040615286"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1145\/1993636.1993674"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0708838104"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2006.07.018"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1080\/15427951.2009.10390643"},{"key":"atypb31","first-page":"110","volume-title":"Combinatorial Algorithms (IWOCA","author":"Chung F.","year":"2014"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0903215107"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2011.06.003"},{"key":"atypb34","first-page":"1277","volume":"11","author":"Dinitz E.","year":"1970","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.13.7.492"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.929958"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511761942"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1515\/jci-2015-0021"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000000067"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1137\/17M1111528"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1137\/141000555"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1137\/090761070"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1145\/1014052.1014068"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000022288.19776.77"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1137\/16M1109345"},{"key":"atypb46","first-page":"175","volume-title":"Proceedings of the 19th Design Automation Conference, ACM","author":"Fiduccia C. M.","year":"1982"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1145\/347090.347121"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1137\/16M1087175"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2016.2637349"},{"key":"atypb50","volume-title":"Code for Experiments of the Present Paper, https:\/\/github.com\/dgleich\/flowpaper-code\/tree\/master\/figures","author":"Fountoulakis K.","year":"2019"},{"key":"atypb51","volume-title":"LocalGraphClustering API, https:\/\/github.com\/kfoynt\/LocalGraphClustering","author":"Fountoulakis K.","year":"2019"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1214-8"},{"key":"atypb53","first-page":"1080","volume-title":"Encyclopedia of Optimization","author":"Frenk H.","year":"2009"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2004.02059.x"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1137\/0218003"},{"key":"atypb56","first-page":"486","volume-title":"Proceedings of the Fifth International AAAI Conference on Weblogs and Social Media","author":"Gargi U.","year":"2011"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1137\/140976649"},{"key":"atypb58","first-page":"1018","volume-title":"Proceedings of the 31st International Conference on Machine Learning, PMLR","author":"Gleich D. F.","year":"2014"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.1145\/2783258.2783376"},{"key":"atypb60","first-page":"191","volume-title":"Handbook of Big Data","author":"Gleich D. F.","year":"2016"},{"key":"atypb61","unstructured":"A. V. Goldberg (1984),\n                      Finding a Maximum Density Subgraph\n                      , M.S. Thesis CSD-84-171, University of California at Berkeley,https:\/\/web.archive.org\/web\/20151129022137\/http:\/\/www.eecs.berkeley.edu\/Pubs\/TechRpts\/1984\/CSD-84-171.pdf."},{"key":"atypb62","doi-asserted-by":"publisher","DOI":"10.1145\/290179.290181"},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1145\/2628036"},{"key":"atypb64","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1111\/j.2517-6161.1989.tb01764.x","volume":"51","author":"Greig D. M.","year":"1989","journal-title":"J. R. Statist. Soc. Ser. B Methodol."},{"key":"atypb65","doi-asserted-by":"publisher","DOI":"10.1137\/110855715"},{"key":"atypb66","first-page":"2687","volume-title":"Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics, PMLR","author":"Ha W.","year":"2020"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1109\/43.159993"},{"key":"atypb68","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.3.219"},{"key":"atypb69","first-page":"3691","volume":"15","author":"Hansen T. J.","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"atypb70","first-page":"2366","volume-title":"Advances in Neural Information Processing Systems 24","author":"Hein M.","year":"2011"},{"key":"atypb71","unstructured":"B. Hendrickson and R. Leland (1994a),\n                      The Chaco User's Guide, Version\n                      2.0, Technical Report SAND94-2692, Sandia National Labs, Albuquerque, NM,https:\/\/cfwebprod.sandia.gov\/cfdocs\/CompResearch\/docs\/guide.pdf."},{"key":"atypb72","doi-asserted-by":"publisher","DOI":"10.1137\/0916028"},{"key":"atypb73","doi-asserted-by":"publisher","DOI":"10.1145\/224170.224228"},{"issue":"9","key":"atypb74","volume":"1","author":"Henzinger A.","year":"2020","journal-title":"ACM J. Exp. Algorithmics, 25, art."},{"key":"atypb75","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1002\/mrm.22177","volume":"63","author":"Hernando D.","year":"2010","journal-title":"Magnetic Reson. Med."},{"key":"atypb76","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2009.80"},{"key":"atypb77","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1120.1126"},{"key":"atypb78","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.10.036"},{"key":"atypb79","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.91.012821"},{"key":"atypb80","doi-asserted-by":"publisher","DOI":"10.1137\/130913250"},{"key":"atypb81","first-page":"290","volume-title":"Proceedings of the 20th International Conference on Machine Learning (ICML-03)","author":"Joachims T.","year":"2003"},{"key":"atypb82","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2019.2953593"},{"key":"atypb83","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2020.3045832"},{"key":"atypb84","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287997"},{"key":"atypb85","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598334138"},{"key":"atypb86","first-page":"1538903","volume":"1145","author":"Khandekar R.","year":"2009","journal-title":"J. ACM, 56, art. 19, https:\/\/doi.org\/10."},{"key":"atypb87","first-page":"463","volume-title":"Proceedings of the 15th International Conference on Neural Information Processing Systems, ACM","author":"Kleinberg J.","year":"2002"},{"key":"atypb88","volume-title":"Algorithm Design","author":"Kleinberg J.","year":"2005"},{"key":"atypb89","doi-asserted-by":"publisher","DOI":"10.1145\/2623330.2623706"},{"key":"atypb90","doi-asserted-by":"publisher","DOI":"10.1145\/2623330.2623621"},{"key":"atypb91","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-55224-3_2"},{"key":"atypb92","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2004.1262177"},{"key":"atypb93","author":"Lancichinetti A.","year":"2009","journal-title":"New J. Phys., 11, art. 033015, https:\/\/doi.org\/10.1088\/1367-2630\/11\/3\/033015."},{"key":"atypb94","first-page":"715","volume-title":"Advances in Neural Information Processing Systems 18 (NIPS2005)","author":"Lang K.","year":"2005"},{"key":"atypb95","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-25960-2_25"},{"key":"atypb96","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02011-7_19"},{"key":"atypb97","doi-asserted-by":"publisher","DOI":"10.3847\/0004-637X\/833\/1\/26"},{"key":"atypb98","volume-title":"Mapping the Similarities of Spectra: Global and Locally-Biased Approaches to SDSS Galaxy Data, preprint, https:\/\/arxiv.org\/abs\/1609.03932","author":"Lawlor D.","year":"2016"},{"key":"atypb99","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"atypb100","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488704"},{"key":"atypb101","volume-title":"Path Finding II: An $\\tilde{\\mathcal{O}}(m \\sqrt{n})$ Algorithm for the Minimum Cost Flow Problem, preprint, https:\/\/arxiv.org\/abs\/1312.6713","author":"Lee Y. T.","year":"2013"},{"key":"atypb102","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1988.21958"},{"key":"atypb103","doi-asserted-by":"publisher","DOI":"10.1145\/331524.331526"},{"key":"atypb104","volume-title":"SNAP Datasets: Stanford Large Network Dataset Collection","author":"Leskovec J.","year":"2014"},{"key":"atypb105","doi-asserted-by":"publisher","DOI":"10.1145\/1367497.1367591"},{"key":"atypb106","doi-asserted-by":"publisher","DOI":"10.1145\/1772690.1772755"},{"key":"atypb107","doi-asserted-by":"publisher","DOI":"10.1080\/15427951.2009.10129177"},{"key":"atypb108","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70139-4"},{"key":"atypb109","doi-asserted-by":"publisher","DOI":"10.1145\/2736277.2741676"},{"key":"atypb110","doi-asserted-by":"publisher","DOI":"10.1137\/120875909"},{"key":"atypb111","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2009.5206871"},{"key":"atypb112","doi-asserted-by":"publisher","DOI":"10.1145\/3357713.3384247"},{"key":"atypb113","doi-asserted-by":"publisher","DOI":"10.1038\/srep01236"},{"key":"atypb114","first-page":"2511","volume":"16","author":"Ma Z.","year":"2018","journal-title":"Experimental Therapeutic Med."},{"key":"atypb115","first-page":"2339","volume":"13","author":"Mahoney M. W.","year":"2012","journal-title":"J. Mach. Learn. Res."},{"key":"atypb116","volume-title":"Graph Cuts and Application to Disparity Map Estmation, https:\/\/web.archive.org\/web\/20221214152458\/https:\/\/imagine.enpc.fr\/~marletr\/enseignement\/mva\/mva-2017\/mva-2017-graphcuts.pdf","author":"Marlet R.","year":"2017"},{"key":"atypb117","doi-asserted-by":"publisher","DOI":"10.1145\/1298306.1298311"},{"key":"atypb118","first-page":"455","volume":"3","author":"Moffat A.","year":"1969","journal-title":"Astron. Astrophys."},{"key":"atypb119","first-page":"8","volume-title":"10th International Workshop on Mining and Learning with Graphs","author":"Namata G.","year":"2012"},{"key":"atypb120","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199206650.001.0001"},{"key":"atypb121","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0601602103"},{"key":"atypb122","first-page":"849","volume-title":"Advances in Neural Information Processing Systems 14","author":"Ng A. Y.","year":"2001"},{"key":"atypb123","first-page":"1141","volume-title":"Proceedings of the 44th Annual ACM Symposium on Theory of Computing","author":"Orecchia L.","year":"2012"},{"key":"atypb124","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973402.94"},{"key":"atypb125","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488705"},{"key":"atypb126","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2013.7.907"},{"key":"atypb127","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/bti115"},{"key":"atypb128","doi-asserted-by":"publisher","DOI":"10.1038\/nature03607"},{"key":"atypb129","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"Papadimitriou C.","year":"1982"},{"key":"atypb130","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974973.49"},{"key":"atypb131","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1602548"},{"key":"atypb132","volume-title":"The Graph-Tool Python Library, figshare","author":"Peixoto T. P.","year":"2014"},{"key":"atypb133","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61142-8_588"},{"key":"atypb134","doi-asserted-by":"publisher","DOI":"10.1137\/0611030"},{"key":"atypb135","doi-asserted-by":"publisher","DOI":"10.1137\/080734315"},{"key":"atypb136","doi-asserted-by":"publisher","DOI":"10.1137\/17M1130046"},{"key":"atypb137","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"atypb138","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-23719-5_40"},{"key":"atypb139","doi-asserted-by":"publisher","DOI":"10.1145\/77600.77620"},{"key":"atypb140","doi-asserted-by":"publisher","DOI":"10.1038\/nature04977"},{"key":"atypb141","doi-asserted-by":"publisher","DOI":"10.1137\/17M1134172"},{"key":"atypb142","doi-asserted-by":"publisher","DOI":"10.1109\/34.868688"},{"key":"atypb143","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-71249-9_39"},{"key":"atypb144","doi-asserted-by":"publisher","DOI":"10.14778\/2994509.2994522"},{"key":"atypb145","doi-asserted-by":"publisher","DOI":"10.1016\/0956-0521(91)90014-V"},{"key":"atypb146","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(83)90006-5"},{"key":"atypb147","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOGO.0000042115.44455.f3"},{"key":"atypb148","doi-asserted-by":"publisher","DOI":"10.1137\/080744888"},{"key":"atypb149","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592050"},{"key":"atypb150","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-009-9471-6"},{"key":"atypb151","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"Tibshirani R.","year":"1996","journal-title":"J. R. Statist. Soc. Ser. B Methodol."},{"key":"atypb152","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2006.70"},{"key":"atypb153","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2011.12.021"},{"key":"atypb154","unstructured":"L. Trevisan (2011),\n                      Combinatorial Optimization: Exact and Approximate Algorithms\n                      , lecture notes for CS261 at Stanford University,https:\/\/web.archive.org\/web\/20200501020454\/http:\/\/theory.stanford.edu\/~trevisan\/books\/cs261.pdf."},{"key":"atypb155","doi-asserted-by":"publisher","DOI":"10.1145\/3038912.3052653"},{"key":"atypb156","doi-asserted-by":"publisher","DOI":"10.1109\/ICIVC.2018.8492887"},{"key":"atypb157","doi-asserted-by":"publisher","DOI":"10.7717\/peerj.453"},{"key":"atypb158","first-page":"1938","volume-title":"International Conference on Machine Learning, JMLR","author":"Veldt L. N.","year":"2016"},{"key":"atypb159","volume-title":"Github software, https:\/\/github.com\/nveldt\/PushRelabelMaxFlow.","author":"Veldt N.","year":"2019"},{"key":"atypb160","doi-asserted-by":"publisher","DOI":"10.1145\/3394486.3403222"},{"key":"atypb161","doi-asserted-by":"publisher","DOI":"10.1137\/20M1321048"},{"key":"atypb162","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975673.43"},{"key":"atypb163","doi-asserted-by":"publisher","DOI":"10.1145\/3308558.3313471"},{"key":"atypb164","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-007-9033-z"},{"key":"atypb165","first-page":"65","volume-title":"Proceedings of ICML Workshop on Unsupervised and Transfer Learning","author":"von Luxburg U.","year":"2012"},{"key":"atypb166","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598337373"},{"key":"atypb167","doi-asserted-by":"publisher","DOI":"10.4203\/csets.17.2"},{"key":"atypb168","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2016.2518687"},{"key":"atypb169","volume-title":"Eileen Collins, https:\/\/en.wikipedia.org\/wiki\/Eileen_Collins [accessed","year":"2021"},{"key":"atypb170","doi-asserted-by":"publisher","DOI":"10.1017\/9781316888568"},{"key":"atypb171","doi-asserted-by":"publisher","DOI":"10.1145\/2501654.2501657"},{"key":"atypb172","doi-asserted-by":"publisher","DOI":"10.1145\/3097983.3098069"},{"key":"atypb173","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2010.5539903"},{"key":"atypb174","first-page":"321","volume-title":"Annual Advances in Neural Information Processing Systems 16: Proceedings of the 2003 Conference","author":"Zhou D.","year":"2004"},{"key":"atypb175","first-page":"912","volume-title":"Proceedings of the 20th International Conference on Machine Learning (ICML-03)","author":"Zhu X.","year":"2003"},{"key":"atypb176","first-page":"396","volume-title":"Proceedings of the 30th International Conference on Machine Learning, JMLR","author":"Zhu Z. A.","year":"2013"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1333055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:34:12Z","timestamp":1787236452000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1333055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2]]},"references-count":176,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1137\/20M1333055"],"URL":"https:\/\/doi.org\/10.1137\/20m1333055","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2]]}}}