{"id":"https://openalex.org/W2922023305","doi":"https://doi.org/10.1145/3357713.3384252","title":"Quadratic speedup for finding marked vertices by Quantum walks","display_name":"Quadratic speedup for finding marked vertices by Quantum walks","publication_year":2020,"publication_date":"2020-06-07","ids":{"openalex":"https://openalex.org/W2922023305","doi":"https://doi.org/10.1145/3357713.3384252","mag":"2922023305"},"language":"en","primary_location":{"id":"doi:10.1145/3357713.3384252","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384252","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.07493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045669197","display_name":"Andris Ambainis","orcid":"https://orcid.org/0000-0002-8716-001X"},"institutions":[{"id":"https://openalex.org/I91123046","display_name":"University of Latvia","ror":"https://ror.org/05g3mes96","country_code":"LV","type":"education","lineage":["https://openalex.org/I91123046"]}],"countries":["LV"],"is_corresponding":false,"raw_author_name":"Andris Ambainis","raw_affiliation_strings":["University of Latvia, Latvia","Univ. of Latvia, Latvia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Latvia, Latvia","institution_ids":["https://openalex.org/I91123046"]},{"raw_affiliation_string":"Univ. of Latvia, Latvia","institution_ids":["https://openalex.org/I91123046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075229372","display_name":"Andr\u00e1s Gily\u00e9n","orcid":"https://orcid.org/0000-0001-5992-5743"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]},{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Gily\u00e9n","raw_affiliation_strings":["QuSoft, Netherlands / CWI, Netherlands / University of Amsterdam, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QuSoft, Netherlands / CWI, Netherlands / University of Amsterdam, Netherlands","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I4210099082","https://openalex.org/I887064364"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033408175","display_name":"Stacey Jeffery","orcid":"https://orcid.org/0000-0003-0046-5089"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]},{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Stacey Jeffery","raw_affiliation_strings":["QuSoft, Netherlands / CWI, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QuSoft, Netherlands / CWI, Netherlands","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I4210099082"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064506362","display_name":"Martins Kokainis","orcid":"https://orcid.org/0000-0003-3381-7271"},"institutions":[{"id":"https://openalex.org/I91123046","display_name":"University of Latvia","ror":"https://ror.org/05g3mes96","country_code":"LV","type":"education","lineage":["https://openalex.org/I91123046"]}],"countries":["LV"],"is_corresponding":false,"raw_author_name":"Martins Kokainis","raw_affiliation_strings":["University of Latvia, Latvia","Univ. of Latvia, Latvia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Latvia, Latvia","institution_ids":["https://openalex.org/I91123046"]},{"raw_affiliation_string":"Univ. of Latvia, Latvia","institution_ids":["https://openalex.org/I91123046"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.346,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.55188789,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"412","last_page":"424"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9819999933242798,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9735000133514404,"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/quadratic-growth","display_name":"Quadratic growth","score":0.9472751617431641},{"id":"https://openalex.org/keywords/quantum-walk","display_name":"Quantum walk","score":0.8947414755821228},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7532132267951965},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.7001787424087524},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6760501861572266},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6260027289390564},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6051360964775085},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.55222088098526},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5093477964401245},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44194725155830383},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4071899950504303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4024038314819336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21075549721717834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13790473341941833},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11096817255020142},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10915091633796692},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09690001606941223}],"concepts":[{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.9472751617431641},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.8947414755821228},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7532132267951965},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.7001787424087524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6760501861572266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6260027289390564},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6051360964775085},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.55222088098526},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5093477964401245},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44194725155830383},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4071899950504303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4024038314819336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21075549721717834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13790473341941833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11096817255020142},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10915091633796692},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09690001606941223},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":10,"locations":[{"id":"doi:10.1145/3357713.3384252","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384252","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/0309bf90-c31e-4005-9ccb-294c09ad4698","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/quadratic-speedup-for-finding-marked-vertices-by-quantum-walks(0309bf90-c31e-4005-9ccb-294c09ad4698).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:arXiv.org:1903.07493","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.07493","pdf_url":"https://arxiv.org/pdf/1903.07493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:cwi.nl:30189","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/30189","pdf_url":"https://ir.cwi.nl/pub/30189/30189.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","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/conferenceObject"},{"id":"mag:2922023305","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.07493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:cwi:oai:cwi.nl:29170","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/29170","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:dare.uva.nl:publications/0309bf90-c31e-4005-9ccb-294c09ad4698","is_oa":false,"landing_page_url":"https://hdl.handle.net/11245.1/0309bf90-c31e-4005-9ccb-294c09ad4698","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"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/conferenceObject"},{"id":"doi:10.48550/arxiv.1903.07493","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.07493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.14288/1.0384619","is_oa":true,"landing_page_url":"https://doi.org/10.14288/1.0384619","pdf_url":null,"source":{"id":"https://openalex.org/S7407053062","display_name":"Open Collections","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Audiovisual"},{"id":"doi:10.5446/57837","is_oa":true,"landing_page_url":"https://doi.org/10.5446/57837","pdf_url":null,"source":{"id":"https://openalex.org/S7407052952","display_name":"TIB KMO / FLOWWORKS GmbH","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Audiovisual"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.07493","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.07493","pdf_url":"https://arxiv.org/pdf/1903.07493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G112975026","display_name":"Quantum algorithms and applications","funder_award_id":"ANR-18-QUAN-0017","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1381843815","display_name":null,"funder_award_id":"QuantAlgo 680-91-034","funder_id":"https://openalex.org/F4320330828","funder_display_name":"QuantERA"},{"id":"https://openalex.org/G1727663806","display_name":null,"funder_award_id":"lzp-2018/1-0173","funder_id":"https://openalex.org/F4320323269","funder_display_name":"Latvijas Zin\u0101tnes Padome"},{"id":"https://openalex.org/G5184048191","display_name":"Quantum algorithms and applications (QuantAlgo)","funder_award_id":"680-91-034","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320323269","display_name":"Latvijas Zin\u0101tnes Padome","ror":"https://ror.org/02ar66p97"},{"id":"https://openalex.org/F4320323297","display_name":"Latvijas Universitate","ror":"https://ror.org/05g3mes96"},{"id":"https://openalex.org/F4320330828","display_name":"QuantERA","ror":null},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1514107797","https://openalex.org/W1561344775","https://openalex.org/W1980458533","https://openalex.org/W1998539366","https://openalex.org/W2006096862","https://openalex.org/W2020918964","https://openalex.org/W2114424556","https://openalex.org/W2151365767","https://openalex.org/W2564579510","https://openalex.org/W2738418152","https://openalex.org/W2740244426","https://openalex.org/W2795534239","https://openalex.org/W2796306990","https://openalex.org/W2805612073","https://openalex.org/W2885549115","https://openalex.org/W3004545975","https://openalex.org/W3104433882","https://openalex.org/W3104890289","https://openalex.org/W4252401180"],"related_works":["https://openalex.org/W1565384686","https://openalex.org/W3098715942","https://openalex.org/W1974252294","https://openalex.org/W2042977557","https://openalex.org/W2079758416","https://openalex.org/W2950262288","https://openalex.org/W2963440986","https://openalex.org/W2185076815","https://openalex.org/W2803761918","https://openalex.org/W1548168548","https://openalex.org/W3158696645","https://openalex.org/W3104625252","https://openalex.org/W3022554509","https://openalex.org/W3184951419","https://openalex.org/W2975721026","https://openalex.org/W853930207","https://openalex.org/W2951262563","https://openalex.org/W3102370491","https://openalex.org/W1558321388","https://openalex.org/W2941476254"],"abstract_inverted_index":{"A":[0],"quantum":[1,27,71],"walk":[2,21,41],"algorithm":[3,22,72],"can":[4],"detect":[5],"the":[6,18,46,50,61,97],"presence":[7],"of":[8,54,63,84],"a":[9,13,32,38,56,69,75,91,103],"marked":[10,33,51,76,85],"vertex":[11,77],"on":[12],"graph":[14],"quadratically":[15,35,94],"faster":[16,36,95],"than":[17,37,96],"corresponding":[19,98],"random":[20,40,100],"(Szegedy,":[23],"FOCS":[24],"2004).":[25],"However,":[26],"algorithms":[28],"that":[29,87,105],"actually":[30],"find":[31],"element":[34],"classical":[39,99],"were":[42],"only":[43],"known":[44],"for":[45,73,109],"special":[47],"case":[48,62],"when":[49],"set":[52,83],"consists":[53],"just":[55],"single":[57],"vertex,":[58],"or":[59],"in":[60,78],"some":[64],"specific":[65],"graphs.":[66],"We":[67],"present":[68],"new":[70],"finding":[74],"any":[79,82],"graph,":[80],"with":[81],"vertices,":[86],"is":[88],"(up":[89],"to":[90],"log":[92],"factor)":[93],"walk,":[101],"resolving":[102],"question":[104],"had":[106],"been":[107],"open":[108],"15":[110],"years.":[111]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}
