{"id":"https://openalex.org/W3033549885","doi":"https://doi.org/10.1007/s10107-020-01522-0","title":"A scaling algorithm for optimizing arbitrary functions over vertices of polytopes","display_name":"A scaling algorithm for optimizing arbitrary functions over vertices of polytopes","publication_year":2020,"publication_date":"2020-06-04","ids":{"openalex":"https://openalex.org/W3033549885","doi":"https://doi.org/10.1007/s10107-020-01522-0","mag":"3033549885"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01522-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01522-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01522-0.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01522-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007996626","display_name":"Sergei Chubanov","orcid":"https://orcid.org/0000-0003-3164-3415"},"institutions":[{"id":"https://openalex.org/I889804353","display_name":"Robert Bosch (Germany)","ror":"https://ror.org/01fe0jt45","country_code":"DE","type":"company","lineage":["https://openalex.org/I889804353"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sergei Chubanov","raw_affiliation_strings":["Bosch Center for Artificial Intelligence, Renningen, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3164-3415","affiliations":[{"raw_affiliation_string":"Bosch Center for Artificial Intelligence, Renningen, Germany","institution_ids":["https://openalex.org/I889804353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007996626"],"corresponding_institution_ids":["https://openalex.org/I889804353"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":0.1458,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.51998267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"190","issue":"1-2","first_page":"89","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8920910358428955},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.7940549850463867},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6777864694595337},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.5963277816772461},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5692529678344727},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.560783326625824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5429782867431641},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5112323760986328},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4962933659553528},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4688645005226135},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.4530094563961029},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4126737117767334},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41250890493392944},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34618914127349854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22539648413658142},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.20278999209403992}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8920910358428955},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.7940549850463867},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6777864694595337},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.5963277816772461},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5692529678344727},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.560783326625824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5429782867431641},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5112323760986328},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4962933659553528},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4688645005226135},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.4530094563961029},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4126737117767334},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41250890493392944},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34618914127349854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22539648413658142},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.20278999209403992},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-020-01522-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01522-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01522-0.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10107-020-01522-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01522-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01522-0.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3033549885.pdf","grobid_xml":"https://content.openalex.org/works/W3033549885.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W166153989","https://openalex.org/W1528072933","https://openalex.org/W1873370420","https://openalex.org/W1985859952","https://openalex.org/W1987985110","https://openalex.org/W2005598280","https://openalex.org/W2031636249","https://openalex.org/W2086875254","https://openalex.org/W2090960684","https://openalex.org/W2133159317","https://openalex.org/W3124896382","https://openalex.org/W3132011969"],"related_works":["https://openalex.org/W2083855693","https://openalex.org/W2158781971","https://openalex.org/W832392341","https://openalex.org/W2184406752","https://openalex.org/W2161977250","https://openalex.org/W169878779","https://openalex.org/W1964839903","https://openalex.org/W1996973635","https://openalex.org/W3004435889","https://openalex.org/W3033549885"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,47],"paper":[3],"we":[4,38],"present":[5],"a":[6],"scaling":[7],"algorithm":[8,48],"for":[9,69],"minimizing":[10],"arbitrary":[11],"functions":[12],"over":[13],"vertices":[14,34],"of":[15,21,55,61,72],"polytopes":[16],"in":[17],"an":[18,25],"oracle":[19,42],"model":[20],"computation":[22],"which":[23],"includes":[24],"augmentation":[26],"oracle.":[27],"For":[28],"the":[29,33,41,70,73],"binary":[30],"case,":[31],"when":[32],"are":[35],"0\u20131":[36],"vectors,":[37],"show":[39],"that":[40],"time":[43],"is":[44],"polynomial.":[45],"Also,":[46],"allows":[49],"us":[50],"to":[51,66],"generalize":[52],"some":[53],"concepts":[54],"combinatorial":[56],"optimization":[57],"concerning":[58],"performance":[59],"bounds":[60,68],"greedy":[62],"algorithms":[63],"and":[64],"leads":[65],"new":[67],"complexity":[71],"simplex":[74],"method.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}