{"id":"https://openalex.org/W2151814155","doi":"https://doi.org/10.1017/s0960129500000360","title":"Categories, relations and dynamic programming","display_name":"Categories, relations and dynamic programming","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2151814155","doi":"https://doi.org/10.1017/s0960129500000360","mag":"2151814155"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129500000360","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129500000360","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"book","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/A5071726140","display_name":"Oege de Moor","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I2802123492","display_name":"Oxford Research Group","ror":"https://ror.org/00z4w4f29","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I2802123492"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Oege De Moor","raw_affiliation_strings":["Programming Research Group, Oxford University Computing Laboratory, 11 Keble Road, Oxford 0X1 3QD, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Programming Research Group, Oxford University Computing Laboratory, 11 Keble Road, Oxford 0X1 3QD, United Kingdom","institution_ids":["https://openalex.org/I2802123492","https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071726140"],"corresponding_institution_ids":["https://openalex.org/I2802123492","https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":5.4512,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.95942702,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"1","first_page":"33","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/functor","display_name":"Functor","score":0.8865324258804321},{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.8176013231277466},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.7725200653076172},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.702703595161438},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.5373090505599976},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5186313986778259},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.48295801877975464},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.45502927899360657},{"id":"https://openalex.org/keywords/extensionality","display_name":"Extensionality","score":0.4462786018848419},{"id":"https://openalex.org/keywords/process-calculus","display_name":"Process calculus","score":0.44134190678596497},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.33524417877197266},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3108547329902649},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.2993471622467041},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24606120586395264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24178892374038696},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18007007241249084}],"concepts":[{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.8865324258804321},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.8176013231277466},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.7725200653076172},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.702703595161438},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.5373090505599976},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5186313986778259},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.48295801877975464},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.45502927899360657},{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.4462786018848419},{"id":"https://openalex.org/C161771561","wikidata":"https://www.wikidata.org/wiki/Q1970286","display_name":"Process calculus","level":2,"score":0.44134190678596497},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.33524417877197266},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3108547329902649},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.2993471622467041},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24606120586395264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24178892374038696},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18007007241249084},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0960129500000360","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129500000360","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"mag:2151814155","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W266714120","https://openalex.org/W636872866","https://openalex.org/W1483728665","https://openalex.org/W1507693023","https://openalex.org/W1513445195","https://openalex.org/W1552647623","https://openalex.org/W1558180172","https://openalex.org/W1559314111","https://openalex.org/W1563218161","https://openalex.org/W1571552128","https://openalex.org/W1600766624","https://openalex.org/W1606100597","https://openalex.org/W1655990431","https://openalex.org/W1965784613","https://openalex.org/W1970026646","https://openalex.org/W1976811743","https://openalex.org/W1977304153","https://openalex.org/W1984503189","https://openalex.org/W1986014102","https://openalex.org/W2002085891","https://openalex.org/W2020938542","https://openalex.org/W2021822788","https://openalex.org/W2027839484","https://openalex.org/W2029671613","https://openalex.org/W2037729105","https://openalex.org/W2045094735","https://openalex.org/W2045323411","https://openalex.org/W2047162848","https://openalex.org/W2048586177","https://openalex.org/W2051228988","https://openalex.org/W2062341684","https://openalex.org/W2064383412","https://openalex.org/W2067978181","https://openalex.org/W2072844988","https://openalex.org/W2073706919","https://openalex.org/W2087817903","https://openalex.org/W2087977785","https://openalex.org/W2096827683","https://openalex.org/W2116908067","https://openalex.org/W2129466151","https://openalex.org/W2133787331","https://openalex.org/W2149574014","https://openalex.org/W2151384546","https://openalex.org/W2152978478","https://openalex.org/W2177760151","https://openalex.org/W2341171179","https://openalex.org/W2751335644","https://openalex.org/W2913026635","https://openalex.org/W2968743833","https://openalex.org/W3110765098","https://openalex.org/W4247177360","https://openalex.org/W4247400007","https://openalex.org/W4251939443","https://openalex.org/W6644701116"],"related_works":["https://openalex.org/W2116908067","https://openalex.org/W1571615440","https://openalex.org/W1559314111","https://openalex.org/W1558180172","https://openalex.org/W2143566245","https://openalex.org/W2057292961","https://openalex.org/W2021257181","https://openalex.org/W1608714802","https://openalex.org/W1600766624","https://openalex.org/W1587758675","https://openalex.org/W2020080707","https://openalex.org/W2172307690","https://openalex.org/W2055669150","https://openalex.org/W1554287520","https://openalex.org/W1507693023","https://openalex.org/W1481153542","https://openalex.org/W2117318327","https://openalex.org/W219888783","https://openalex.org/W1536939176","https://openalex.org/W1511110335"],"abstract_inverted_index":{"Dynamic":[0],"programming":[1,23,49,63,79,203],"is":[2,33,88,97,133,148,196,204,222,246,295],"a":[3,85,128,137,143,149,162,175,230,240,265,280],"strategy":[4],"for":[5,124],"solving":[6],"optimisation":[7],"problems.":[8],"In":[9,81,229],"this":[10,109,177,292],"paper,":[11],"we":[12,233,258,276],"show":[13],"how":[14],"many":[15],"problems":[16],"that":[17,198,218,275,287],"may":[18],"be":[19,52,155,189,285],"solved":[20],"by":[21,41,54,206],"dynamic":[22,48,62,202],"are":[24,117,271,277],"instances":[25,118],"of":[26,38,61,66,119,139,168,179,201,209,215,224,237],"the":[27,36,73,82,101,165,199,207,213,235],"same":[28],"abstract":[29],"specification.":[30],"This":[31,243],"specification":[32,60],"phrased":[34],"using":[35],"calculus":[37],"relations":[39,140],"offered":[40],"topos":[42,102],"theory.":[43],"The":[44,58,105,254],"main":[45],"theorem":[46],"underlying":[47],"can":[50,154,188,284],"then":[51],"proved":[53,286],"straightforward":[55],"equational":[56],"reasoning.":[57],"generic":[59],"makes":[64],"use":[65,200],"higher-order":[67],"operators":[68,75],"on":[69,100,174],"relations,":[70],"akin":[71],"to":[72,113,135,161,171,193,227,250,264,297],"fold":[74,120,187],"found":[76],"in":[77,252,279,299],"functional":[78],"languages.":[80],"present":[83],"context,":[84],"data":[86],"type":[87],"modelled":[89],"as":[90,239],"an":[91,98,172,219],"initial":[92,110,183],"F":[93,96,111,115],"-algebra,":[94],"where":[95],"endofunctor":[99,173],"under":[103],"consideration.":[104],"mediating":[106],"arrows":[107],"from":[108,191],"-algebra":[112],"other":[114],"-algebras":[116],"\u2013":[121],"but":[122,248],"only":[123],"total":[125],"functions.":[126],"For":[127],"regular":[129,146],"category":[130,138],"\u03b5,":[131],"it":[132,153,283],"possible":[134],"construct":[136],"Rel(\u03b5).":[141],"When":[142],"functor":[144,163],"between":[145,164],"categories":[147,167],"so-called":[150],"relator":[151],",":[152],"extended":[156],"(in":[157],"some":[158],"canonical":[159],"way)":[160],"corresponding":[166],"relations.":[169,194],"Applied":[170],"topos,":[176,282],"process":[178],"extending":[180],"functors":[181],"preserves":[182],"algebras,":[184],"and":[185,267,291],"hence":[186],"generalised":[190],"functions":[192],"It":[195],"well-known":[197],"governed":[205],"principle":[208,214,236],"optimality":[210,216,238],".":[211],"Roughly,":[212],"says":[217],"optimal":[220,225],"solution":[221],"composed":[223],"solutions":[226],"subproblems.":[228],"first":[231],"attempt,":[232],"formalise":[234],"distributivity":[241,244],"condition.":[242],"condition":[245,294],"elegant,":[247],"difficult":[249],"check":[251],"practice.":[253,300],"difficulty":[255],"arises":[256],"because":[257],"consider":[259],"minimum":[260,269],"elements":[261,270],"with":[262],"respect":[263],"preorder,":[266],"therefore":[268],"not":[272],"unique.":[273],"Assuming":[274],"working":[278],"Boolean":[281],"monotonicity":[288,293],"implies":[289],"distributivity,":[290],"easy":[296],"verify":[298]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
