{"id":"https://openalex.org/W1992720234","doi":"https://doi.org/10.1137/s0097539796304220","title":"Structure in Approximation Classes","display_name":"Structure in Approximation Classes","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1992720234","doi":"https://doi.org/10.1137/s0097539796304220","mag":"1992720234"},"language":"en","primary_location":{"id":"pmh:oai:iris.uniroma1.it:11573/48862","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/48862","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"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/A5012362492","display_name":"Pierluigi Crescenzi","orcid":"https://orcid.org/0000-0001-8789-3195"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"CRESCENZI P.","raw_affiliation_strings":["Dipartimento di Scienze dell'Informazione, Universit\u00e0 degli Studi di Roma \u201cLa Sapienza\u201d Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze dell'Informazione, Universit\u00e0 degli Studi di Roma \u201cLa Sapienza\u201d Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003972927","display_name":"Viggo Kann","orcid":"https://orcid.org/0000-0003-3199-8953"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"KANN V.","raw_affiliation_strings":["Department of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":null,"display_name":"TREVISAN L.","orcid":null},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"TREVISAN L.","raw_affiliation_strings":["Dipartimento di Scienze dell'Informazione, Universit\u00e0 degli Studi di Roma \u201cLa Sapienza\u201d Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze dell'Informazione, Universit\u00e0 degli Studi di Roma \u201cLa Sapienza\u201d Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056847255","display_name":"Riccardo Silvestri","orcid":null},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"SILVESTRI, RICCARDO","raw_affiliation_strings":["Dipartimento di Scienze dell'Informazione, Universit\u00e0 degli Studi di Roma \u201cLa Sapienza\u201d Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze dell'Informazione, Universit\u00e0 degli Studi di Roma \u201cLa Sapienza\u201d Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7568,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.97574402,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T10142","display_name":"Formal Methods in Verification","score":0.9986000061035156,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9962000250816345,"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/approximation-algorithm","display_name":"Approximation algorithm","score":0.758364200592041},{"id":"https://openalex.org/keywords/apx","display_name":"APX","score":0.7498189210891724},{"id":"https://openalex.org/keywords/hardness-of-approximation","display_name":"Hardness of approximation","score":0.58614581823349},{"id":"https://openalex.org/keywords/l-reduction","display_name":"L-reduction","score":0.5654096007347107},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5376135110855103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5089893341064453},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.448879212141037},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.43754842877388},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40203556418418884},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.38723766803741455},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3095572888851166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24536815285682678},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08729636669158936}],"concepts":[{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.758364200592041},{"id":"https://openalex.org/C130698151","wikidata":"https://www.wikidata.org/wiki/Q4653447","display_name":"APX","level":4,"score":0.7498189210891724},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.58614581823349},{"id":"https://openalex.org/C62114133","wikidata":"https://www.wikidata.org/wiki/Q5366944","display_name":"L-reduction","level":5,"score":0.5654096007347107},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5376135110855103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5089893341064453},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.448879212141037},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43754842877388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40203556418418884},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38723766803741455},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3095572888851166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24536815285682678},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08729636669158936},{"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/C181199279","wikidata":"https://www.wikidata.org/wiki/Q8047","display_name":"Enzyme","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162008176","wikidata":"https://www.wikidata.org/wiki/Q419305","display_name":"Peroxidase","level":3,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:iris.uniroma1.it:11573/48862","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/48862","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W201661424","https://openalex.org/W1511894390","https://openalex.org/W1591000087","https://openalex.org/W1972345639","https://openalex.org/W1974647909","https://openalex.org/W1975790950","https://openalex.org/W2001564241","https://openalex.org/W2004660767","https://openalex.org/W2011039300","https://openalex.org/W2022212237","https://openalex.org/W2036265926","https://openalex.org/W2036879409","https://openalex.org/W2038225707","https://openalex.org/W2040924621","https://openalex.org/W2052936500","https://openalex.org/W2053094807","https://openalex.org/W2053651631","https://openalex.org/W2059453880","https://openalex.org/W2060079637","https://openalex.org/W2063158069","https://openalex.org/W2072181151","https://openalex.org/W2074417667","https://openalex.org/W2082160108","https://openalex.org/W2084732248","https://openalex.org/W2100308637","https://openalex.org/W2102669784","https://openalex.org/W2105195422","https://openalex.org/W2110256264","https://openalex.org/W2116940701","https://openalex.org/W2118711349","https://openalex.org/W2123068254","https://openalex.org/W2136500328","https://openalex.org/W2143391442","https://openalex.org/W2148793850","https://openalex.org/W2150636758","https://openalex.org/W2160785839","https://openalex.org/W3022694456","https://openalex.org/W4229492708","https://openalex.org/W4237363759","https://openalex.org/W4255515059"],"related_works":["https://openalex.org/W4245749626","https://openalex.org/W1970705056","https://openalex.org/W2072802070","https://openalex.org/W2084935502","https://openalex.org/W1992720234","https://openalex.org/W2011285766","https://openalex.org/W4253115531","https://openalex.org/W11978745","https://openalex.org/W2050896380","https://openalex.org/W1577145008"],"abstract_inverted_index":{"The":[0,27],"study":[1],"of":[2,6,24,34,45,62,85,113,121,138],"the":[3,18,22,32,83,110,118,131,135],"approximability":[4,132],"properties":[5,133],"NP-hard":[7],"optimization":[8,37],"problems":[9,38,116],"has":[10],"recently":[11],"made":[12],"great":[13],"advances":[14],"mainly":[15],"due":[16],"to":[17,99],"results":[19,81],"obtained":[20],"in":[21,55],"field":[23],"proof":[25],"checking.":[26],"last":[28],"important":[29,36],"breakthrough":[30],"proves":[31],"APX-completeness":[33],"several":[35,86],"and":[39,49,117,134],"thus":[40],"reconciles":[41],"\"two":[42],"distinct":[43],"views":[44],"approximation":[46,88,96,104],"classes:":[47],"syntactic":[48],"computational\"":[50],"[S.":[51],"Khanna":[52],"et":[53],"al.,":[54],"Proc.":[56],"35th":[57],"IEEE":[58,65],"Symp.":[59],"on":[60,82],"Foundations":[61],"Computer":[63,66],"Science,":[64],"Society":[67],"Press,":[68],"Los":[69],"Alamitos,":[70],"CA,":[71],"1994,":[72],"pp.":[73],"819--830].":[74],"In":[75,90],"this":[76],"paper":[77],"we":[78,108,126],"obtain":[79],"new":[80,95,128],"structure":[84],"computationally-defined":[87],"classes.":[89],"particular,":[91],"after":[92],"defining":[93],"a":[94],"preserving":[97],"reducibility":[98],"be":[100],"used":[101],"for":[102],"asmany":[103],"classes":[105],"as":[106],"possible,":[107],"give":[109],"first":[111,119],"examples":[112,120],"natural":[114,122],"NPO-complete":[115],"APX-intermediate":[123],"problems.":[124,140],"Moreover,":[125],"state":[127],"connections":[129],"between":[130],"query":[136],"complexity":[137],"NPO":[139]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6}],"updated_date":"2026-06-03T06:16:58.514037","created_date":"2025-10-10T00:00:00"}
