{"id":"https://openalex.org/W4399567638","doi":"https://doi.org/10.1007/s00453-024-01238-z","title":"Approximate and Randomized Algorithms for Computing a Second Hamiltonian Cycle","display_name":"Approximate and Randomized Algorithms for Computing a Second Hamiltonian Cycle","publication_year":2024,"publication_date":"2024-06-12","ids":{"openalex":"https://openalex.org/W4399567638","doi":"https://doi.org/10.1007/s00453-024-01238-z"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-024-01238-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01238-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01238-z.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01238-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048361071","display_name":"Argyrios Deligkas","orcid":"https://orcid.org/0000-0002-6513-6748"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Argyrios Deligkas","raw_affiliation_strings":["Department of Computer Science, Royal Holloway University of London, Egham, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Royal Holloway University of London, Egham, UK","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018078197","display_name":"George B. Mertzios","orcid":"https://orcid.org/0000-0001-7182-585X"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"George B. Mertzios","raw_affiliation_strings":["Department of Computer Science, Durham University, Durham, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Durham University, Durham, UK","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011756177","display_name":"Paul G. Spirakis","orcid":"https://orcid.org/0000-0001-5396-3749"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paul G. Spirakis","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047948708","display_name":"Viktor Zamaraev","orcid":"https://orcid.org/0000-0001-5755-4141"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Viktor Zamaraev","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018078197"],"corresponding_institution_ids":["https://openalex.org/I190082696"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3547,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60035419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"86","issue":"9","first_page":"2766","last_page":"2785"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/algorithm","display_name":"Algorithm","score":0.8025949597358704},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.44984978437423706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44913119077682495},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.4424741566181183},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3552815020084381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3192840814590454},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2437213659286499}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.8025949597358704},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.44984978437423706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44913119077682495},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.4424741566181183},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3552815020084381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3192840814590454},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2437213659286499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00453-024-01238-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01238-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01238-z.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:durham-repository.worktribe.com:1897832","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1897832","pdf_url":"https://durham-repository.worktribe.com/file/1897832/1/Published%20Journal%20Article%20%28Advance%20Online%20Version%29","source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s00453-024-01238-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01238-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01238-z.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5260088266","display_name":"Algorithmic Aspects of Temporal Graphs","funder_award_id":"EP/P02002X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6811041424","display_name":"Algorithmic Aspects of Temporal Graphs","funder_award_id":"EP/P020372/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6979527396","display_name":null,"funder_award_id":"EP/P02002X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8719353587","display_name":null,"funder_award_id":"EP/P0","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G967227458","display_name":null,"funder_award_id":"EP/P020372/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320323","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399567638.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1504855246","https://openalex.org/W1564921898","https://openalex.org/W1968952709","https://openalex.org/W1969186119","https://openalex.org/W1971483538","https://openalex.org/W1990218616","https://openalex.org/W1995621089","https://openalex.org/W2007351870","https://openalex.org/W2012438638","https://openalex.org/W2027410688","https://openalex.org/W2028767175","https://openalex.org/W2037002007","https://openalex.org/W2048163742","https://openalex.org/W2066542589","https://openalex.org/W2088096994","https://openalex.org/W2096056318","https://openalex.org/W2120141762","https://openalex.org/W2169359757","https://openalex.org/W2508797883","https://openalex.org/W2794350243","https://openalex.org/W2963537887","https://openalex.org/W3141776272","https://openalex.org/W4238913085","https://openalex.org/W4241301040"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"In":[1,99,458],"this":[2,97,100],"paper":[3,101],"we":[4,24,102,116,306,442],"consider":[5,117],"the":[6,54,71,104,119,242,273,294,325,430],"following":[7],"problem:":[8],"Given":[9],"a":[10,16,26,82,108,122,151,156,229,233,279,284,299,356,448],"Hamiltonian":[11,17,28,84,110,286,358,450],"graph":[12,56,296],"G":[13,21,46,57,66,297,329],",":[14,22,47,199,291,323,354,478],"and":[15,48,139,239],"cycle":[18,29,85,111,125,157,287,359,451],"C":[19],"of":[20,45,65,106,121,173,232,244,272,328],"can":[23,360,443],"compute":[25,444],"second":[27,83,109,123,270,285,357,449],"$$C^{\\prime":[30,158],"}":[31,159,247],"\\ne":[32,160],"C$$":[33,161],"<mml:math":[34,135,144,162,180,206,250,313,338,375,401,435,466,485],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[35,136,145,163,181,207,251,314,339,376,402,436,467,486],"<mml:mrow>":[36,164,182,208,212,217,252,259,315,340,377,403,408,416,468,489],"<mml:msup>":[37,165,387,414,487],"<mml:mi>C</mml:mi>":[38,42,166,170],"<mml:mo>\u2032</mml:mo>":[39,167],"</mml:msup>":[40,168,390,421],"<mml:mo>\u2260</mml:mo>":[41,169],"</mml:mrow>":[43,171,197,216,221,223,265,266,321,352,395,412,420,422,476],"</mml:math>":[44,138,147,172,198,224,267,322,353,396,423,438,477],"if":[49,62,70,324],"yes,":[50],"how":[51],"quickly?":[52],"If":[53],"input":[55,295],"satisfies":[58],"certain":[59],"conditions":[60],"(e.g.":[61],"every":[63,310],"vertex":[64],"is":[67,74,78,94,275,330,439],"odd,":[68],"or":[69],"minimum":[72,131,302,326,431],"degree":[73,132,141,327,432],"large":[75,300],"enough),":[76],"it":[77],"known":[79,95,455],"that":[80,293,308],"such":[81],"always":[86],"exists.":[87],"Despite":[88],"substantial":[89],"efforts,":[90],"no":[91],"subexponential-time":[92],"algorithm":[93,153,281,481],"for":[96,154,309],"problem.":[98],"relax":[103],"problem":[105,274],"computing":[107,155],"in":[112,241,397,483],"two":[113],"ways.":[114],"First,":[115],"approximating":[118],"length":[120,174],"longest":[124],"on":[126],"n":[127],"-vertex":[128],"graphs":[129],"with":[130,288,363,445],"$$\\delta":[133,433,461],"$$":[134,143,374,434],"<mml:mi>\u03b4</mml:mi>":[137,218,255,437,469],"maximum":[140],"$$\\Delta":[142],"<mml:mi>\u0394</mml:mi>":[146,213,254],".":[148,225,268],"We":[149,277],"provide":[150],"linear-time":[152],"at":[175,331,365],"least":[176,332,366],"$$n-4\\alpha":[177],"(\\sqrt{n}+2\\alpha":[178],")+8$$":[179],"<mml:mi>n</mml:mi>":[183,189,262,349,382,410,419,474],"<mml:mo>-</mml:mo>":[184,214,219,379],"<mml:mn>4</mml:mn>":[185,351,389,417],"<mml:mi>\u03b1</mml:mi>":[186,193,209],"<mml:mo>(</mml:mo>":[187,260,409,472],"<mml:msqrt>":[188,261,346],"</mml:msqrt>":[190,263,348],"<mml:mo>+</mml:mo>":[191,195,350,392],"<mml:mn>2</mml:mn>":[192,215,220,415,488],"<mml:mo>)</mml:mo>":[194,264,411,475],"<mml:mn>8</mml:mn>":[196,342,347],"where":[200],"$$\\alpha":[201],"=":[202,248,462],"\\frac{\\Delta":[203],"-2}{\\delta":[204],"-2}$$":[205],"<mml:mo>=</mml:mo>":[210,257,470],"<mml:mfrac>":[211,253,341,380,385],"</mml:mfrac>":[222,256,344,383,391],"This":[226,425],"results":[227],"provides":[228],"constructive":[230],"proof":[231],"recent":[234],"result":[235,426],"by":[236],"Gir\u00e3o,":[237],"Kittipassorn,":[238],"Narayanan":[240],"regime":[243],"$$\\frac{\\Delta":[245],"}{\\delta":[246],"o(\\sqrt{n})$$":[249],"<mml:mi>o</mml:mi>":[258,405,490],"Our":[269],"relaxation":[271],"probabilistic.":[276],"propose":[278],"randomized":[280],"which":[282],"computes":[283],"high":[289,446],"probability":[290,364,447],"given":[292],"has":[298],"enough":[301],"degree.":[303],"More":[304],"specifically,":[305],"prove":[307],"$$0&lt;p\\le":[311],"0.02$$":[312],"<mml:mn>0</mml:mn>":[316],"<mml:mo>&lt;</mml:mo>":[317],"<mml:mi>p</mml:mi>":[318,343,388,404,418],"<mml:mo>\u2264</mml:mo>":[319],"<mml:mn>0.02</mml:mn>":[320],"$$\\frac{8}{p}":[333],"\\log":[334],"\\sqrt{8}n":[335],"+":[336,371],"4$$":[337],"<mml:mo>log</mml:mo>":[345,473],"then":[355],"be":[361],"computed":[362],"$$1":[367],"-":[368],"\\frac{1}{n}\\left(":[369],"\\frac{50}{p^4}":[370],"1":[372],"\\right)":[373],"<mml:mn>1</mml:mn>":[378,381,393],"<mml:mfenced>":[384],"<mml:mn>50</mml:mn>":[386],"</mml:mfenced>":[394],"$$poly(n)":[398],"\\cdot":[399],"2^{4pn}$$":[400],"<mml:mi>l</mml:mi>":[406],"<mml:mi>y</mml:mi>":[407],"<mml:mo>\u00b7</mml:mo>":[413],"time.":[424],"implies":[427],"that,":[428],"when":[429,460],"sufficiently":[440],"large,":[441],"faster":[452],"than":[453],"any":[454],"deterministic":[456],"algorithm.":[457],"particular,":[459],"\\omega":[463],"(\\log":[464],"n)$$":[465],"<mml:mi>\u03c9</mml:mi>":[471],"our":[479],"probabilistic":[480],"works":[482],"$$2^{o(n)}$$":[484]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
