{"day":"06","language":[{"iso":"eng"}],"author":[{"first_name":"Da Wei","last_name":"Zheng","full_name":"Zheng, Da Wei"},{"orcid":"0000-0002-5008-6530","last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.09217","open_access":"1"}],"year":"2024","abstract":[{"lang":"eng","text":"We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1-E)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time 0(mE-1), beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in 0(mE-1 log E-1). Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-E)-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is 0(mE-1), where m is the sum of the number of initially existing and inserted edges."}],"oa":1,"quality_controlled":"1","date_published":"2024-03-06T00:00:00Z","scopus_import":"1","publication_identifier":{"eissn":["1436-4646"],"issn":["0025-5610"]},"article_processing_charge":"No","title":"Multiplicative auction algorithm for approximate maximum weight bipartite matching","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"13236"}]},"citation":{"mla":"Zheng, Da Wei, and Monika H. Henzinger. “Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching.” <i>Mathematical Programming</i>, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s10107-024-02066-3\">10.1007/s10107-024-02066-3</a>.","ista":"Zheng DW, Henzinger MH. 2024. Multiplicative auction algorithm for approximate maximum weight bipartite matching. Mathematical Programming.","ieee":"D. W. Zheng and M. H. Henzinger, “Multiplicative auction algorithm for approximate maximum weight bipartite matching,” <i>Mathematical Programming</i>. Springer Nature, 2024.","apa":"Zheng, D. W., &#38; Henzinger, M. H. (2024). Multiplicative auction algorithm for approximate maximum weight bipartite matching. <i>Mathematical Programming</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10107-024-02066-3\">https://doi.org/10.1007/s10107-024-02066-3</a>","chicago":"Zheng, Da Wei, and Monika H Henzinger. “Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching.” <i>Mathematical Programming</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10107-024-02066-3\">https://doi.org/10.1007/s10107-024-02066-3</a>.","ama":"Zheng DW, Henzinger MH. Multiplicative auction algorithm for approximate maximum weight bipartite matching. <i>Mathematical Programming</i>. 2024. doi:<a href=\"https://doi.org/10.1007/s10107-024-02066-3\">10.1007/s10107-024-02066-3</a>","short":"D.W. Zheng, M.H. Henzinger, Mathematical Programming (2024)."},"publication":"Mathematical Programming","publication_status":"epub_ahead","month":"03","date_created":"2024-03-17T23:00:58Z","external_id":{"arxiv":["2301.09217"]},"publisher":"Springer Nature","article_type":"original","status":"public","_id":"15121","acknowledgement":"The first author thanks Chandra Chekuri for useful discussions about this paper. This work was done in part at the University of Vienna. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564 “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project “Fast Algorithms for a Reactive Network Layer (ReactNet)”, P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_updated":"2024-03-19T08:32:32Z","oa_version":"Preprint","department":[{"_id":"MoHe"}],"doi":"10.1007/s10107-024-02066-3","project":[{"grant_number":"101019564","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures"},{"grant_number":"P33775 ","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}]}