{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-08-20T22:01:14Z","oa_version":"Published Version","oa":1,"scopus_import":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","status":"public","quality_controlled":"1","title":"Faster submodular maximization for several classes of matroids","alternative_title":["LIPIcs"],"day":"01","type":"conference","file":[{"date_updated":"2023-08-21T07:04:36Z","file_size":930943,"date_created":"2023-08-21T07:04:36Z","success":1,"file_id":"14090","checksum":"a5eef225014e003efbfbe4830fdd23cb","relation":"main_file","access_level":"open_access","creator":"dernst","file_name":"2023_LIPIcsICALP_HenzingerM.pdf","content_type":"application/pdf"}],"date_updated":"2023-08-21T07:05:47Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"07","article_processing_charge":"Yes","date_published":"2023-07-01T00:00:00Z","publication_status":"published","abstract":[{"text":"The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint has been investigated extensively due to its algorithmic properties and expressive power. Though tight approximation algorithms for general matroid constraints exist in theory, the running times of such algorithms typically scale quadratically, and are not practical for truly large scale settings. Recent progress has focused on fast algorithms for important classes of matroids given in explicit form. Currently, nearly-linear time algorithms only exist for graphic and partition matroids [Alina Ene and Huy L. Nguyen, 2019]. In this work, we develop algorithms for monotone submodular maximization constrained by graphic, transversal matroids, or laminar matroids in time near-linear in the size of their representation. Our algorithms achieve an optimal approximation of 1-1/e-ε and both generalize and accelerate the results of Ene and Nguyen [Alina Ene and Huy L. Nguyen, 2019]. In fact, the running time of our algorithm cannot be improved within the fast continuous greedy framework of Badanidiyuru and Vondrák [Ashwinkumar Badanidiyuru and Jan Vondrák, 2014].\r\nTo achieve near-linear running time, we make use of dynamic data structures that maintain bases with approximate maximum cardinality and weight under certain element updates. These data structures need to support a weight decrease operation and a novel Freeze operation that allows the algorithm to freeze elements (i.e. force to be contained) in its basis regardless of future data structure operations. For the laminar matroid, we present a new dynamic data structure using the top tree interface of Alstrup, Holm, de Lichtenberg, and Thorup [Stephen Alstrup et al., 2005] that maintains the maximum weight basis under insertions and deletions of elements in O(log n) time. This data structure needs to support certain subtree query and path update operations that are performed every insertion and deletion that are non-trivial to handle in conjunction. For the transversal matroid the Freeze operation corresponds to requiring the data structure to keep a certain set S of vertices matched, a property that we call S-stability. While there is a large body of work on dynamic matching algorithms, none are S-stable and maintain an approximate maximum weight matching under vertex updates. We give the first such algorithm for bipartite graphs with total running time linear (up to log factors) in the number of edges.","lang":"eng"}],"department":[{"_id":"MoHe"}],"volume":261,"intvolume":"       261","year":"2023","file_date_updated":"2023-08-21T07:04:36Z","acknowledgement":" Monika Henzinger: This project has received funding from the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant\r\nagreement No. 101019564 “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project “Static and Dynamic Hierarchical Graph Decompositions”, I 5982-N, and project “Fast Algorithms for a Reactive Network Layer (ReactNet)”, P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. Jan Vondrák: Supported by NSF Award 2127781.","project":[{"call_identifier":"H2020","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982"},{"grant_number":"P33775 ","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"ddc":["000"],"has_accepted_license":"1","author":[{"last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"full_name":"Liu, Paul","first_name":"Paul","last_name":"Liu"},{"full_name":"Vondrák, Jan","first_name":"Jan","last_name":"Vondrák"},{"full_name":"Zheng, Da Wei","first_name":"Da Wei","last_name":"Zheng"}],"publication":"50th International Colloquium on Automata, Languages, and Programming","doi":"10.4230/LIPIcs.ICALP.2023.74","publication_identifier":{"isbn":["9783959772785"],"issn":["18688969"]},"external_id":{"arxiv":["2305.00122"]},"citation":{"mla":"Henzinger, Monika H., et al. “Faster Submodular Maximization for Several Classes of Matroids.” <i>50th International Colloquium on Automata, Languages, and Programming</i>, vol. 261, 74, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.74\">10.4230/LIPIcs.ICALP.2023.74</a>.","ieee":"M. H. Henzinger, P. Liu, J. Vondrák, and D. W. Zheng, “Faster submodular maximization for several classes of matroids,” in <i>50th International Colloquium on Automata, Languages, and Programming</i>, Paderborn, Germany, 2023, vol. 261.","ista":"Henzinger MH, Liu P, Vondrák J, Zheng DW. 2023. Faster submodular maximization for several classes of matroids. 50th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LIPIcs, vol. 261, 74.","apa":"Henzinger, M. H., Liu, P., Vondrák, J., &#38; Zheng, D. W. (2023). Faster submodular maximization for several classes of matroids. In <i>50th International Colloquium on Automata, Languages, and Programming</i> (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.74\">https://doi.org/10.4230/LIPIcs.ICALP.2023.74</a>","chicago":"Henzinger, Monika H, Paul Liu, Jan Vondrák, and Da Wei Zheng. “Faster Submodular Maximization for Several Classes of Matroids.” In <i>50th International Colloquium on Automata, Languages, and Programming</i>, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.74\">https://doi.org/10.4230/LIPIcs.ICALP.2023.74</a>.","ama":"Henzinger MH, Liu P, Vondrák J, Zheng DW. Faster submodular maximization for several classes of matroids. In: <i>50th International Colloquium on Automata, Languages, and Programming</i>. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.74\">10.4230/LIPIcs.ICALP.2023.74</a>","short":"M.H. Henzinger, P. Liu, J. Vondrák, D.W. Zheng, in:, 50th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023."},"conference":{"end_date":"2023-07-14","location":"Paderborn, Germany","start_date":"2023-07-10","name":"ICALP: International Colloquium on Automata, Languages, and Programming"},"ec_funded":1,"_id":"14086","article_number":"74","language":[{"iso":"eng"}]}