{"id":"https://openalex.org/W7165037039","doi":"https://doi.org/10.48550/arxiv.2606.17732","title":"Four-Cycle Counting in Low-Degeneracy Graph Streams","display_name":"Four-Cycle Counting in Low-Degeneracy Graph Streams","publication_year":2026,"publication_date":"2026-06-16","ids":{"openalex":"https://openalex.org/W7165037039","doi":"https://doi.org/10.48550/arxiv.2606.17732"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.17732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17732","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.17732","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122137647","display_name":"Sebastian L\u00fcderssen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L\u00fcderssen, Sebastian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008120721","display_name":"Stefan Neumann","orcid":"https://orcid.org/0000-0002-3981-1500"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neumann, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138804450","display_name":"Pan Peng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Pan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.3935000002384186,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.3935000002384186,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.2702000141143799,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.15379999577999115,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/matching","display_name":"Matching (statistics)","score":0.4848000109195709},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44119998812675476},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42160001397132874},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.3873000144958496},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.3831000030040741},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.35929998755455017},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.3431999981403351},{"id":"https://openalex.org/keywords/blossom-algorithm","display_name":"Blossom algorithm","score":0.3366999924182892},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.3231000006198883}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4973999857902527},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4848000109195709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45809999108314514},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3928000032901764},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3725999891757965},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.35929998755455017},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.3431999981403351},{"id":"https://openalex.org/C61455927","wikidata":"https://www.wikidata.org/wiki/Q1030529","display_name":"Blossom algorithm","level":3,"score":0.3366999924182892},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C89198739","wikidata":"https://www.wikidata.org/wiki/Q3079880","display_name":"Data stream mining","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C100107663","wikidata":"https://www.wikidata.org/wiki/Q1516988","display_name":"Hopcroft\u2013Karp algorithm","level":5,"score":0.3075999915599823},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2847999930381775},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.17732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17732","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.17732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17732","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,18,117],"study":[1],"the":[2,6,44,50,57,75],"problem":[3],"of":[4,8,46,52,124],"$(1+\\varepsilon)$-approximating":[5],"number":[7,45,51],"four-cycles":[9,95,150],"in":[10,111],"graphs":[11,169],"given":[12],"as":[13,171],"arbitrary":[14],"order":[15],"edge":[16],"streams.":[17,127],"propose":[19],"two":[20],"new":[21],"algorithms":[22,120,163],"based":[23],"on":[24,121,167],"sampling":[25],"induced":[26],"subgraphs.":[27],"Our":[28,84],"first":[29],"contribution":[30,86],"is":[31,43,49,56,68,87,109,147],"a":[32,88,122,141],"two-pass":[33,129],"algorithm":[34,61,90,130,146],"that":[35,91],"uses":[36],"$\\widetilde{O}(\u03bam":[37],"/":[38],"\\sqrt{T})$":[39],"space,":[40],"where":[41],"$m$":[42],"edges,":[47,103],"$T$":[48],"four-cycles,":[53],"and":[54,67,114],"$\u03ba$":[55],"graph's":[58],"degeneracy.":[59],"This":[60],"improves":[62],"upon":[63],"existing":[64],"theoretical":[65,156],"bounds":[66],"provably":[69],"optimal":[70],"for":[71],"constant-degeneracy":[72],"graphs,":[73],"matching":[74,154],"known":[76],"$\u03a9(m/\\sqrt{T})$":[77],"lower":[78],"bound":[79],"up":[80],"to":[81,139],"lower-order":[82],"factors.":[83],"second":[85],"one-pass":[89,145],"remains":[92],"accurate":[93],"when":[94,149],"are":[96,151],"not":[97],"highly":[98],"concentrated":[99],"around":[100],"individual":[101],"nodes,":[102],"or":[104],"wedges;":[105],"this":[106],"structural":[107],"property":[108],"common":[110],"sparse":[112],"social":[113,172],"collaboration":[115],"networks.":[116,173],"evaluate":[118],"both":[119],"variety":[123],"real-world":[125],"graph":[126],"The":[128,144],"consistently":[131],"outperforms":[132],"state-of-the-art":[133],"methods,":[134],"using":[135],"substantially":[136],"less":[137],"space":[138],"achieve":[140],"desired":[142],"accuracy.":[143],"competitive":[148],"evenly":[152],"distributed,":[153],"our":[155,162],"analysis.":[157],"Unlike":[158],"several":[159],"recent":[160],"works,":[161],"perform":[164],"well":[165],"even":[166],"non-bipartite":[168],"such":[170]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-18T00:00:00"}
