{"id":"https://openalex.org/W50901504","doi":"https://doi.org/10.1007/978-3-540-76796-1_11","title":"Recent Developments in Discrete Convex Analysis","display_name":"Recent Developments in Discrete Convex Analysis","publication_year":2008,"publication_date":"2008-11-06","ids":{"openalex":"https://openalex.org/W50901504","doi":"https://doi.org/10.1007/978-3-540-76796-1_11","mag":"50901504"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-76796-1_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-76796-1_11","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Research Trends in Combinatorial Optimization","raw_type":"book-chapter"},"type":"book-chapter","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/A5032957138","display_name":"Kazuo Murota","orcid":"https://orcid.org/0000-0003-1518-9152"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuo Murota","raw_affiliation_strings":["Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032957138"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":4.2183,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.93253629,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"219","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9970999956130981,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9970999956130981,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.7589014768600464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6067317128181458},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.48919677734375},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.48307564854621887},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46793386340141296},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.4608362317085266},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.44022342562675476},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.41116976737976074},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3695034980773926},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33989161252975464},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3074833154678345},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10163804888725281}],"concepts":[{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.7589014768600464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6067317128181458},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.48919677734375},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.48307564854621887},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46793386340141296},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.4608362317085266},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.44022342562675476},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.41116976737976074},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3695034980773926},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33989161252975464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3074833154678345},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10163804888725281}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-540-76796-1_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-76796-1_11","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Research Trends in Combinatorial Optimization","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.472.9343","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.472.9343","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/METR08-31.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":106,"referenced_works":["https://openalex.org/W39126767","https://openalex.org/W110875287","https://openalex.org/W389907844","https://openalex.org/W612917828","https://openalex.org/W617723651","https://openalex.org/W1483973251","https://openalex.org/W1498671329","https://openalex.org/W1506292197","https://openalex.org/W1520461790","https://openalex.org/W1522351268","https://openalex.org/W1526731700","https://openalex.org/W1533712308","https://openalex.org/W1539230026","https://openalex.org/W1547992467","https://openalex.org/W1557310162","https://openalex.org/W1576820654","https://openalex.org/W1589059132","https://openalex.org/W1680189815","https://openalex.org/W1807235826","https://openalex.org/W1968865391","https://openalex.org/W1972946082","https://openalex.org/W1978185401","https://openalex.org/W1978696336","https://openalex.org/W1983932475","https://openalex.org/W1989453388","https://openalex.org/W1989801809","https://openalex.org/W1998867815","https://openalex.org/W2000743971","https://openalex.org/W2002430844","https://openalex.org/W2011193572","https://openalex.org/W2013303693","https://openalex.org/W2015553537","https://openalex.org/W2020338529","https://openalex.org/W2023061756","https://openalex.org/W2024063662","https://openalex.org/W2025350305","https://openalex.org/W2027307783","https://openalex.org/W2027588132","https://openalex.org/W2033329811","https://openalex.org/W2033885045","https://openalex.org/W2035186046","https://openalex.org/W2043507681","https://openalex.org/W2049688189","https://openalex.org/W2049715533","https://openalex.org/W2050548031","https://openalex.org/W2057904949","https://openalex.org/W2059470728","https://openalex.org/W2059663227","https://openalex.org/W2059664817","https://openalex.org/W2061647611","https://openalex.org/W2063885213","https://openalex.org/W2065591019","https://openalex.org/W2066894529","https://openalex.org/W2068115726","https://openalex.org/W2068200970","https://openalex.org/W2071453418","https://openalex.org/W2071703764","https://openalex.org/W2072291569","https://openalex.org/W2074514032","https://openalex.org/W2074891551","https://openalex.org/W2075976548","https://openalex.org/W2079530391","https://openalex.org/W2079988604","https://openalex.org/W2085855437","https://openalex.org/W2091861938","https://openalex.org/W2093903916","https://openalex.org/W2094571546","https://openalex.org/W2097406041","https://openalex.org/W2106772662","https://openalex.org/W2107547393","https://openalex.org/W2112148168","https://openalex.org/W2116987486","https://openalex.org/W2120092158","https://openalex.org/W2123812125","https://openalex.org/W2129866531","https://openalex.org/W2134750400","https://openalex.org/W2142363911","https://openalex.org/W2143529993","https://openalex.org/W2155598645","https://openalex.org/W2157867221","https://openalex.org/W2158486393","https://openalex.org/W2158907148","https://openalex.org/W2166838615","https://openalex.org/W2171578835","https://openalex.org/W2214712460","https://openalex.org/W2304678994","https://openalex.org/W2340149117","https://openalex.org/W2482182218","https://openalex.org/W2757107770","https://openalex.org/W2800852802","https://openalex.org/W2949889366","https://openalex.org/W2962711478","https://openalex.org/W2988480584","https://openalex.org/W4206054140","https://openalex.org/W4210391498","https://openalex.org/W4210431029","https://openalex.org/W4210767642","https://openalex.org/W4233212183","https://openalex.org/W4235234911","https://openalex.org/W4241764762","https://openalex.org/W4242255739","https://openalex.org/W4242336842","https://openalex.org/W4249667877","https://openalex.org/W4302334632","https://openalex.org/W4388212639","https://openalex.org/W6619320498"],"related_works":["https://openalex.org/W2133925519","https://openalex.org/W2026600343","https://openalex.org/W1878643722","https://openalex.org/W1601341493","https://openalex.org/W2913596570","https://openalex.org/W4214795209","https://openalex.org/W4214969932","https://openalex.org/W2134356220","https://openalex.org/W868123585","https://openalex.org/W1557678201"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}