{"id":"https://openalex.org/W4403794792","doi":"https://doi.org/10.48550/arxiv.2409.16688","title":"Cycle Counting under Local Differential Privacy for Degeneracy-bounded Graphs","display_name":"Cycle Counting under Local Differential Privacy for Degeneracy-bounded Graphs","publication_year":2024,"publication_date":"2024-09-25","ids":{"openalex":"https://openalex.org/W4403794792","doi":"https://doi.org/10.48550/arxiv.2409.16688"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2409.16688","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.16688","pdf_url":"https://arxiv.org/pdf/2409.16688","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2409.16688","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092595887","display_name":"Quentin Hillebrand","orcid":"https://orcid.org/0000-0002-7747-4998"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hillebrand, Quentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038811120","display_name":"Vorapong Suppakitpaisarn","orcid":"https://orcid.org/0000-0002-7020-395X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suppakitpaisarn, Vorapong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043159528","display_name":"Tetsuo Shibuya","orcid":"https://orcid.org/0000-0003-1514-5766"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shibuya, Tetsuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9886000156402588,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9886000156402588,"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/T12288","display_name":"Optimization and Search Problems","score":0.9674000144004822,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9187999963760376,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.8503355383872986},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7808998227119446},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.7592852115631104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4981212615966797},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.47758248448371887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4459114670753479},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35487115383148193},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3489546775817871},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1831052601337433},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1124851405620575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10054731369018555},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05947396159172058}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.8503355383872986},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7808998227119446},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.7592852115631104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4981212615966797},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.47758248448371887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4459114670753479},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35487115383148193},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3489546775817871},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1831052601337433},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1124851405620575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10054731369018555},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05947396159172058},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2409.16688","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.16688","pdf_url":"https://arxiv.org/pdf/2409.16688","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2409.16688","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2409.16688","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:2409.16688","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2409.16688","pdf_url":"https://arxiv.org/pdf/2409.16688","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4403794792.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3038283795","https://openalex.org/W2604501336","https://openalex.org/W2734500670","https://openalex.org/W2558166297","https://openalex.org/W2372940580","https://openalex.org/W2315671126","https://openalex.org/W798507144","https://openalex.org/W2964481303","https://openalex.org/W1751413323","https://openalex.org/W4207069403"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2,70,83,86,124],"algorithm":[3,68,84,122],"for":[4,14,184],"counting":[5,23,67],"the":[6,24,29,34,45,50,55,63,99,104,108,149,161],"number":[7,25,46,56,162],"of":[8,26,37,47,57,59,72,89,107,127,140,151,163,165],"cycles":[9,58,164],"under":[10,28],"local":[11],"differential":[12],"privacy":[13,30],"degeneracy-bounded":[15,111,185],"input":[16],"graphs.":[17,186],"Numerous":[18],"studies":[19],"have":[20],"focused":[21],"on":[22],"triangles":[27,141],"notion,":[31],"demonstrating":[32],"that":[33,146],"expected":[35,87,125],"$\\ell_2$-error":[36,88,126],"these":[38],"algorithms":[39],"is":[40,44,98,103,136],"$\u03a9(n^{1.5})$,":[41],"where":[42,96],"$n$":[43],"nodes":[48],"in":[49,117],"graph.":[51,109],"When":[52],"parameterized":[53],"by":[54],"length":[60,166],"four":[61],"($C_4$),":[62],"best":[64],"existing":[65],"triangle":[66],"has":[69],"error":[71],"$O(n^{1.5}":[73],"+":[74,92,176],"\\sqrt{C_4})":[75],"=":[76,130,182],"O(n^2)$.":[77],"In":[78],"this":[79],"paper,":[80],"we":[81],"introduce":[82],"with":[85],"$O(\u03b4^{1.5}":[90],"n^{0.5}":[91],"\u03b4^{0.5}":[93],"d_{\\max}^{0.5}":[94,174],"n^{0.5})$,":[95],"$\u03b4$":[97],"degeneracy":[100],"and":[101],"$d_{\\max}$":[102],"maximum":[105],"degree":[106,150],"For":[110],"graphs":[112],"($\u03b4\\in":[113],"\u0398(1)$)":[114],"commonly":[115],"found":[116],"practical":[118],"social":[119],"networks,":[120],"our":[121],"achieves":[123],"$O(d_{\\max}^{0.5}":[128,180],"n^{0.5})":[129],"O(n)$.":[131],"Our":[132],"algorithm's":[133],"core":[134],"idea":[135],"a":[137,143,169],"precise":[138],"count":[139],"following":[142],"preprocessing":[144],"step":[145],"approximately":[147],"sorts":[148],"all":[152],"nodes.":[153],"This":[154],"approach":[155],"can":[156],"be":[157],"extended":[158],"to":[159],"approximate":[160],"$k$,":[167],"maintaining":[168],"similar":[170],"$\\ell_2$-error,":[171],"namely":[172],"$O(\u03b4^{(k-2)/2}":[173],"n^{(k-2)/2}":[175],"\u03b4^{k/2}":[177],"n^{(k-2)/2})$":[178],"or":[179],"n^{(k-2)/2})":[181],"O(n^{(k-1)/2})$":[183]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-10-27T00:00:00"}