{"id":"https://openalex.org/W2020338529","doi":"https://doi.org/10.1142/s1793830909000063","title":"ON THE PIPAGE ROUNDING ALGORITHM FOR SUBMODULAR FUNCTION MAXIMIZATION \u2014 A VIEW FROM DISCRETE CONVEX ANALYSIS","display_name":"ON THE PIPAGE ROUNDING ALGORITHM FOR SUBMODULAR FUNCTION MAXIMIZATION \u2014 A VIEW FROM DISCRETE CONVEX ANALYSIS","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2020338529","doi":"https://doi.org/10.1142/s1793830909000063","mag":"2020338529"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830909000063","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830909000063","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067169957","display_name":"Akiyoshi Shioura","orcid":"https://orcid.org/0000-0002-5216-7190"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"AKIYOSHI SHIOURA","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067169957"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":1.0571,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.7652611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"01","issue":"01","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.9684270620346069},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.8831691741943359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7508180141448975},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.710857093334198},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.6417651176452637},{"id":"https://openalex.org/keywords/concave-function","display_name":"Concave function","score":0.5969270467758179},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5705385804176331},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5514142513275146},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5160946249961853},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5127642750740051},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4907630383968353},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.4900404214859009},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.43751367926597595},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.41737374663352966},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3733522295951843},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33336079120635986},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.28091102838516235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1475350558757782}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.9684270620346069},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8831691741943359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7508180141448975},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.710857093334198},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.6417651176452637},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.5969270467758179},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5705385804176331},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5514142513275146},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5160946249961853},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5127642750740051},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4907630383968353},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.4900404214859009},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.43751367926597595},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.41737374663352966},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3733522295951843},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33336079120635986},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28091102838516235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1475350558757782},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s1793830909000063","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830909000063","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.503.6487","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.503.6487","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dais.is.tohoku.ac.jp/~shioura/papers/dmaa09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.617.3825","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.617.3825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.keisu.t.u-tokyo.ac.jp/research/techrep/data/2008/METR08-03.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1498671329","https://openalex.org/W1576820654","https://openalex.org/W1579522749","https://openalex.org/W1662047737","https://openalex.org/W1680189815","https://openalex.org/W1989453388","https://openalex.org/W1995275762","https://openalex.org/W2011193572","https://openalex.org/W2012329067","https://openalex.org/W2015553537","https://openalex.org/W2021907424","https://openalex.org/W2029873790","https://openalex.org/W2033885045","https://openalex.org/W2035186046","https://openalex.org/W2035575256","https://openalex.org/W2042275390","https://openalex.org/W2059664817","https://openalex.org/W2068200970","https://openalex.org/W2072291569","https://openalex.org/W2080656989","https://openalex.org/W2087770658","https://openalex.org/W2100440346","https://openalex.org/W2123812125","https://openalex.org/W2128059732","https://openalex.org/W2287460576","https://openalex.org/W2304678994","https://openalex.org/W2340149117","https://openalex.org/W2482182218","https://openalex.org/W2621717961","https://openalex.org/W2757107770","https://openalex.org/W2962711478","https://openalex.org/W2988480584","https://openalex.org/W4206054140","https://openalex.org/W4293860921"],"related_works":["https://openalex.org/W2963059222","https://openalex.org/W4289237892","https://openalex.org/W2964314169","https://openalex.org/W2735578456","https://openalex.org/W2020338529","https://openalex.org/W2354484762","https://openalex.org/W2902154658","https://openalex.org/W2416404459","https://openalex.org/W2946234094","https://openalex.org/W4289285151"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,25,34,56,65,83,93,100,126,129,147,153,161,167,171],"problem":[3],"of":[4,27,58,67,71,85,95,102,114,128,131,155,173],"maximizing":[5],"a":[6,12,50,76,112,136,142,174],"nondecreasing":[7,175],"submodular":[8,59,96,176],"set":[9],"function":[10,177],"under":[11],"matroid":[13],"constraint.":[14],"Recently,":[15],"Calinescu":[16],"et":[17],"al.":[18],"(2007)":[19],"proposed":[20],"an":[21,179,185],"elegant":[22],"framework":[23,47],"for":[24,55,145,152],"approximation":[26,168],"this":[28,46,80],"problem,":[29],"which":[30,61,98],"is":[31],"based":[32],"on":[33,79,160],"pipage":[35,148],"rounding":[36,149],"technique":[37],"by":[38,89,119],"Ageev":[39],"and":[40,43,121,124],"Sviridenko":[41],"(2004),":[42],"showed":[44],"that":[45],"indeed":[48],"yields":[49],"(1":[51],"-":[52],"1/e)-approximation":[53],"algorithm":[54,150,169],"class":[57,94,113,127],"functions":[60,70,97,110,117,134],"are":[62,99,111],"represented":[63],"as":[64,135],"sum":[66,101,130,154],"weighted":[68,132,156],"rank":[69,133,157],"matroids.":[72],"This":[73,182],"paper":[74],"sheds":[75],"new":[77,162],"light":[78],"result":[81,140],"from":[82],"viewpoint":[84],"discrete":[86,115],"convex":[87],"analysis":[88],"extending":[90],"it":[91],"to":[92,170],"M":[103,107],"\u266e":[104,108],"-concave":[105,109],"functions.":[106,158],"concave":[116],"introduced":[118],"Murota":[120],"Shioura":[122],"(1999),":[123],"contain":[125],"proper":[137],"subclass.":[138],"Our":[139],"provides":[141],"better":[143],"understanding":[144],"why":[146],"works":[151],"Based":[159],"observation,":[163],"we":[164],"further":[165],"extend":[166],"maximization":[172],"over":[178],"integral":[180],"polymatroid.":[181],"extension":[183],"has":[184],"application":[186],"in":[187],"multi-unit":[188],"combinatorial":[189],"auctions.":[190]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
