{"id":"https://openalex.org/W1914315659","doi":"https://doi.org/10.1145/2897518.2897571","title":"Separating subadditive euclidean functionals","display_name":"Separating subadditive euclidean functionals","publication_year":2016,"publication_date":"2016-06-10","ids":{"openalex":"https://openalex.org/W1914315659","doi":"https://doi.org/10.1145/2897518.2897571","mag":"1914315659"},"language":"en","primary_location":{"id":"doi:10.1145/2897518.2897571","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897518.2897571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-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/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Carnegie Mellon University, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054318475","display_name":"Wesley Pegden","orcid":"https://orcid.org/0000-0002-3680-1817"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wesley Pegden","raw_affiliation_strings":["Carnegie Mellon University, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056950019"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0066215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"7","issue":null,"first_page":"22","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T12288","display_name":"Optimization and Search Problems","score":0.9994999766349792,"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/T11106","display_name":"Data Management and Algorithms","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematics","display_name":"Mathematics","score":0.8211263418197632},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7813645601272583},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.7552808523178101},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6703916788101196},{"id":"https://openalex.org/keywords/subadditivity","display_name":"Subadditivity","score":0.576569676399231},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5361172556877136},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5239360928535461},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5189849734306335},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5025675296783447},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.473335325717926},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.4692858159542084},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4634634554386139},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.4589901566505432},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.445297509431839},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.41440582275390625},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.27704912424087524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1408824920654297},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09276294708251953},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0893864631652832}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8211263418197632},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7813645601272583},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.7552808523178101},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6703916788101196},{"id":"https://openalex.org/C19220575","wikidata":"https://www.wikidata.org/wiki/Q1934099","display_name":"Subadditivity","level":2,"score":0.576569676399231},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5361172556877136},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5239360928535461},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5189849734306335},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5025675296783447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.473335325717926},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.4692858159542084},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4634634554386139},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.4589901566505432},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.445297509431839},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.41440582275390625},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.27704912424087524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1408824920654297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09276294708251953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0893864631652832},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2897518.2897571","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897518.2897571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W16274536","https://openalex.org/W175627016","https://openalex.org/W626292722","https://openalex.org/W1501328773","https://openalex.org/W1551519020","https://openalex.org/W1964683996","https://openalex.org/W1981700549","https://openalex.org/W1986758236","https://openalex.org/W1993966762","https://openalex.org/W1995157426","https://openalex.org/W1995274002","https://openalex.org/W1996075091","https://openalex.org/W2009803313","https://openalex.org/W2011240422","https://openalex.org/W2012329067","https://openalex.org/W2014068360","https://openalex.org/W2017995040","https://openalex.org/W2023830447","https://openalex.org/W2040257225","https://openalex.org/W2045762410","https://openalex.org/W2055569927","https://openalex.org/W2058748455","https://openalex.org/W2058937865","https://openalex.org/W2060484774","https://openalex.org/W2092569613","https://openalex.org/W2116402476","https://openalex.org/W2121599632","https://openalex.org/W2122103820","https://openalex.org/W2151977393","https://openalex.org/W2160442083","https://openalex.org/W2399100674","https://openalex.org/W2950473912","https://openalex.org/W2963958826","https://openalex.org/W2989661724","https://openalex.org/W4210556995","https://openalex.org/W4211015501"],"related_works":["https://openalex.org/W2184834902","https://openalex.org/W2183097989","https://openalex.org/W2241463327","https://openalex.org/W2038458261","https://openalex.org/W2105006450","https://openalex.org/W1579502333","https://openalex.org/W2044119054","https://openalex.org/W2129011715","https://openalex.org/W2529553768","https://openalex.org/W2798081993"],"abstract_inverted_index":{"The":[0],"classical":[1],"Beardwood-Halton-Hammersly":[2],"theorem":[3],"(1959)":[4],"asserts":[5],"the":[6,13,21,34,39,45,62,79,88,101,106,125,166,176],"existence":[7,46],"of":[8,12,24,47,72],"an":[9],"asymptotic":[10],"formula":[11],"form":[14],"constant":[15],"times":[16],"square":[17,64,90],"root":[18],"n":[19,30,84],"for":[20,53,182],"minimum":[22,80,102,107],"length":[23,81,103,108],"a":[25],"Traveling":[26],"Salesperson":[27],"Tour":[28],"through":[29,83],"random":[31,59,85,128],"points":[32,60,86,129],"in":[33,38,61,87,130,171],"unit":[35,63,89],"square,":[36],"and":[37,115,139,144],"decades":[40],"since":[41],"it":[42,75],"was":[43,91],"proved,":[44],"such":[48,55,99],"formulas":[49],"has":[50],"been":[51],"shown":[52],"other":[54,140],"Euclidean":[56,131],"functionals":[57],"on":[58,127,154],"as":[65,100,111],"well.":[66],"Despite":[67],"more":[68],"than":[69],"50":[70],"years":[71],"attention,":[73],"however,":[74],"remained":[76],"unknown":[77],"whether":[78],"TSP":[82,126,167],"asymptotically":[92,135],"distinct":[93,136],"from":[94,117,137],"its":[95,118],"natural":[96,141,156],"lower":[97,142,157,180],"bounds,":[98,143],"spanning":[104],"tree,":[105],"2-factor,":[109],"or,":[110],"raised":[112],"by":[113],"Goemans":[114],"Bertsimas,":[116],"linear":[119],"programming":[120],"relaxation.":[121],"We":[122],"prove":[123],"that":[124,146,150],"space":[132],"is":[133,175],"indeed":[134],"these":[138,155,183],"show":[145],"this":[147],"separation":[148],"implies":[149],"branch-and-bound":[151,184],"algorithms":[152],"based":[153],"bounds":[158],"must":[159],"take":[160],"nearly":[161],"exponential":[162],"time":[163],"to":[164,168],"solve":[165],"optimality,":[169],"even":[170],"average":[172],"case.":[173],"This":[174],"first":[177],"average-case":[178],"superpolynomial":[179],"bound":[181],"algorithms.":[185]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}