{"id":"https://openalex.org/W4417355700","doi":"https://doi.org/10.48550/arxiv.2506.10758","title":"Circulant TSP: Vertices of the Edge-Length Polytope and Superpolynomial Lower Bounds","display_name":"Circulant TSP: Vertices of the Edge-Length Polytope and Superpolynomial Lower Bounds","publication_year":2025,"publication_date":"2025-06-12","ids":{"openalex":"https://openalex.org/W4417355700","doi":"https://doi.org/10.48550/arxiv.2506.10758"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.10758","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.10758","pdf_url":"https://arxiv.org/pdf/2506.10758","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.10758","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044065045","display_name":"Samuel C. Gutekunst","orcid":"https://orcid.org/0000-0002-3516-2996"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gutekunst, Samuel C.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044065045"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.38029998540878296,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.38029998540878296,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.17389999330043793,"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.12309999763965607,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.8363000154495239},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7019000053405762},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5827999711036682},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5339000225067139},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.5166000127792358},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.4350999891757965},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.41440001130104065},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.3952000141143799}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8363000154495239},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8310999870300293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7940999865531921},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7019000053405762},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5827999711036682},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5339000225067139},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44920000433921814},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.4350999891757965},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.39250001311302185},{"id":"https://openalex.org/C119677069","wikidata":"https://www.wikidata.org/wiki/Q4846249","display_name":"Integer factorization","level":4,"score":0.3734999895095825},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3675000071525574},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.34209999442100525},{"id":"https://openalex.org/C82190004","wikidata":"https://www.wikidata.org/wiki/Q5121633","display_name":"Circulant graph","level":5,"score":0.3172000050544739},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2628999948501587}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.10758","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.10758","pdf_url":"https://arxiv.org/pdf/2506.10758","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},{"id":"doi:10.48550/arxiv.2506.10758","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.10758","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.10758","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.10758","pdf_url":"https://arxiv.org/pdf/2506.10758","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,11,23,53,87,91,127,154,172],"edge-length":[3,68],"polytope,":[4],"motivated":[5],"both":[6],"by":[7],"algorithmic":[8],"research":[9,20],"on":[10,44,62,153,166],"Circulant":[12,26,138],"Traveling":[13],"Salesman":[14],"Problem":[15],"(Circulant":[16],"TSP)":[17],"and":[18,42,78,102],"number-theoretic":[19],"related":[21,170],"to":[22,73,86,171],"Buratti-Horak-Rosa":[24,173],"conjecture.":[25],"TSP":[27,33,76,130],"is":[28,37,83,100,107,120,146],"a":[29,38,108,113,121,140,184],"special":[30],"case":[31],"of":[32,55,89,93,116,123,156,179],"whose":[34],"overall":[35],"complexity":[36],"significant":[39],"still-open":[40],"question,":[41],"where":[43],"an":[45,56,159],"input":[46],"with":[47,96,103],"vertices":[48,94,117],"$\\{1,":[49],"2,":[50],"...,":[51],"n\\}$,":[52],"cost":[54],"edge":[57,180],"$\\{i,":[58],"j\\}$":[59],"depends":[60],"only":[61],"its":[63],"length":[64],"$\\min\\{|i-j|,":[65],"n-|i-j|\\}$.":[66],"The":[67],"polytope":[69],"provides":[70],"one":[71],"path":[72],"solving":[74],"circulant":[75],"instances,":[77],"we":[79,162],"show":[80],"that":[81],"it":[82],"intimately":[84],"connected":[85],"factorization":[88,155],"$n$:":[90],"number":[92,115],"scales":[95],"$n$":[97,99,106,119],"whenever":[98,105,118],"prime":[101],"$n^{3/2}$":[104],"prime-squared,":[109],"but":[110],"there":[111],"are":[112],"superpolynomial":[114,164],"power":[122],"2.":[124],"In":[125],"contrast,":[126],"more-standard":[128],"Symmetric":[129],"Polytope":[131],"has":[132],"roughly":[133],"$n!$":[134],"vertices.":[135],"Hence,":[136],"for":[137],"TSP,":[139],"brute-force":[141],"algorithm":[142],"checking":[143],"every":[144],"vertex":[145],"actually":[147],"efficient":[148],"in":[149],"some":[150],"cases,":[151],"based":[152],"$n$.":[157],"As":[158],"intermediate":[160],"step,":[161],"give":[163],"lower-bounds":[165],"two":[167],"combinatorial":[168],"sequences":[169],"conjecture,":[174],"which":[175],"asks":[176],"what":[177],"combinations":[178],"lengths":[181],"can":[182],"comprise":[183],"Hamiltonian":[185],"path.":[186]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}