{"id":"https://openalex.org/W7150777833","doi":"https://doi.org/10.48550/arxiv.2604.02949","title":"Sample compression schemes for balls in structurally sparse graphs","display_name":"Sample compression schemes for balls in structurally sparse graphs","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7150777833","doi":"https://doi.org/10.48550/arxiv.2604.02949"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.02949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02949","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.02949","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090509291","display_name":"Romain Bourneuf","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bourneuf, Romain","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133005465","display_name":"J\u0119drzej Hodor","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hodor, J\u0119drzej","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133003652","display_name":"Piotr Micek","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micek, Piotr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133017519","display_name":"Cl\u00e9ment Rambaud","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rambaud, Cl\u00e9ment","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.33160001039505005,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.33160001039505005,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.2903999984264374,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.04800000041723251,"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/hypergraph","display_name":"Hypergraph","score":0.8622000217437744},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7541000247001648},{"id":"https://openalex.org/keywords/compression","display_name":"Compression (physics)","score":0.5471000075340271},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.5465999841690063},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.5012000203132629},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4375},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.41760000586509705},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4032999873161316}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8622000217437744},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7541000247001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.723800003528595},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5853999853134155},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.5471000075340271},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.5465999841690063},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.5012000203132629},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4950000047683716},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4375},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3671000003814697},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2815999984741211}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.02949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02949","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.02949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02949","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"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":{"Sample":[0],"compression":[1,23,71,89,115,193],"schemes":[2,133],"were":[3],"defined":[4],"by":[5,142],"Littlestone":[6],"and":[7,100,144,207,220],"Warmuth":[8],"(1986)":[9],"as":[10],"an":[11,225],"abstraction":[12],"of":[13,31,33,62,68,76,91,109,117,125,156,178,185,195,218,230],"the":[14,40,50,60,63,74,82,139,154,157,167,183,204,209,216],"structure":[15],"underlying":[16],"many":[17],"learning":[18],"algorithms.":[19],"In":[20],"a":[21,28,34,54,69,87,113,122,162,190],"sample":[22,30,51,70,88,114,159,192],"scheme,":[24],"we":[25,57,135,150,171,223],"are":[26,146],"given":[27],"large":[29],"vertices":[32],"fixed":[35],"hypergraph":[36,85,108,184],"with":[37,86,166],"labels":[38,61],"indicating":[39],"containment":[41],"in":[42,52,81,130,187],"some":[43],"hyperedge.":[44],"The":[45,66,132],"task":[46],"is":[47,73,79,200],"to":[48,138,203],"compress":[49],"such":[53],"way":[55],"that":[56,78,106,134,149,173,213],"can":[58],"retrieve":[59,151],"original":[64,158,168],"sample.":[65],"size":[67,93,196],"scheme":[72,90,116,194],"amount":[75],"information":[77],"kept":[80],"compression.":[83],"Every":[84],"bounded":[92,96,110,118],"must":[94],"have":[95],"VC-dimension.":[97],"Conversely,":[98],"Moran":[99,143,219],"Yehudayoff":[101],"(J.":[102],"ACM,":[103],"2016)":[104],"showed":[105],"every":[107,175],"VC-dimension":[111],"admits":[112],"size.":[119],"We":[120],"study":[121],"specific":[123],"class":[124],"hypergraphs":[126],"emerging":[127],"from":[128,215],"balls":[129,186],"graphs.":[131],"construct":[136],"(contrary":[137],"ones":[140],"constructed":[141],"Yehudayoff)":[145],"\\textit{proper},":[147],"meaning":[148],"not":[152],"only":[153],"labeling":[155],"but":[160],"also":[161],"hyperedge":[163],"(ball)":[164],"consistent":[165],"labeling.":[169],"First,":[170],"prove":[172,224],"for":[174,228],"graph":[176],"$G$":[177,188],"treewidth":[179],"at":[180,232],"most":[181,233],"$t$,":[182],"has":[189],"proper":[191],"$\\mathcal{O}(t\\log":[197],"t)$;":[198],"this":[199],"tight":[201],"up":[202],"logarithmic":[205],"factor":[206],"improves":[208],"quadratic":[210],"(improper)":[211],"bound":[212],"follows":[214],"result":[217,227],"Yehudayoff.":[221],"Second,":[222],"analogous":[226],"graphs":[229],"cliquewidth":[231],"$t$.":[234]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-07T00:00:00"}
