{"id":"https://openalex.org/W4396570303","doi":"https://doi.org/10.4230/lipics.icalp.2024.137","title":"On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification","display_name":"On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4396570303","doi":"https://doi.org/10.4230/lipics.icalp.2024.137"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2404.18904","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.18904","pdf_url":"https://arxiv.org/pdf/2404.18904","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2404.18904","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061236440","display_name":"Jakub Gajarsk\u00fd","orcid":"https://orcid.org/0000-0002-4761-3432"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Gajarsk\u00fd, Jakub","raw_affiliation_strings":["University of Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-4761-3432","affiliations":[{"raw_affiliation_string":"University of Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027138320","display_name":"Rose McCarty","orcid":"https://orcid.org/0000-0002-9884-3406"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"McCarty, Rose","raw_affiliation_strings":["School of Mathematics and School of Computer Science, Georgia Institute of Technology, Altanta, GA, USA"],"raw_orcid":"https://orcid.org/0000-0002-9884-3406","affiliations":[{"raw_affiliation_string":"School of Mathematics and School of Computer Science, Georgia Institute of Technology, Altanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.97079998254776,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.97079998254776,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9549000263214111,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9438999891281128,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7989838123321533},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.725959300994873},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6168990731239319},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5312343239784241},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5158652663230896},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3565453290939331},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3288690745830536}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7989838123321533},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.725959300994873},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6168990731239319},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5312343239784241},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5158652663230896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3565453290939331},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3288690745830536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2404.18904","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.18904","pdf_url":"https://arxiv.org/pdf/2404.18904","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:20280","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.137","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol297-icalp2024/LIPIcs.ICALP.2024.137/LIPIcs.ICALP.2024.137.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"InProceedings"},{"id":"doi:10.48550/arxiv.2404.18904","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2404.18904","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":"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"},{"id":"doi:10.4230/lipics.icalp.2024.137","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2024.137","pdf_url":null,"source":{"id":"https://openalex.org/S4393917817","display_name":"Leibniz international proceedings in informatics","issn_l":"1868-8969","issn":["1868-8969"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2404.18904","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.18904","pdf_url":"https://arxiv.org/pdf/2404.18904","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G580598315","display_name":"PostDoctoral Research Fellowship","funder_award_id":"2202961","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"},{"id":"https://openalex.org/F4320332869","display_name":"College of Computing","ror":"https://ror.org/01zkghx44"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396570303.pdf","grobid_xml":"https://content.openalex.org/works/W4396570303.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4386900933","https://openalex.org/W2980963558","https://openalex.org/W4229058035","https://openalex.org/W3125672081","https://openalex.org/W4385301946","https://openalex.org/W2006389905"],"abstract_inverted_index":{"Graph":[0],"classes":[1,24,31,46,58,84,102,113,117,216,219],"of":[2,12,20,29,32,44,47,54,72,85,100,103,111,118,141,169,188,203,220,222],"bounded":[3,33,36,48,86,104,223],"tree":[4,105,119,142,170],"rank":[5,120,143,171],"were":[6],"introduced":[7],"recently":[8],"in":[9,115,137,218],"the":[10,13,186,193,201],"context":[11],"model":[14],"checking":[15],"problem":[16],"for":[17,56,82,180,214],"first-order":[18],"logic":[19],"graphs.":[21],"These":[22],"graph":[23,30,45,83,101,112,116,133,139,162,167,215],"are":[25,40],"a":[26,41,52,69,77,109,138,149,160,165,181],"common":[27],"generalization":[28],"degree":[34],"and":[35,38,59,80],"treedepth,":[37],"they":[39],"special":[42],"case":[43],"expansion.":[49],"We":[50,95,107],"introduce":[51],"notion":[53],"decomposition":[55,74,81],"these":[57,62],"show":[60],"that":[61,153,176,199],"decompositions":[63],"can":[64],"be":[65],"efficiently":[66],"computed.":[67],"Also,":[68],"natural":[70],"extension":[71],"our":[73,123,189],"leads":[75,125],"to":[76,126,154],"new":[78],"characterization":[79,110,124],"expansion":[87],"(and":[88],"an":[89,127,211],"efficient":[90,128,195],"algorithm":[91,152],"computing":[92],"this":[93,191],"decomposition).":[94],"then":[96],"focus":[97],"on":[98],"interpretations":[99],"rank.":[106],"give":[108],"interpretable":[114,136,217],"2.":[121],"Importantly,":[122],"sparsification":[129],"procedure:":[130],"For":[131],"any":[132,155],"class":[134,140,168],"\ud835\udc9e":[135,158],"at":[144,172],"most":[145,173],"2,":[146],"there":[147],"is":[148,192],"polynomial":[150],"time":[151],"G":[156,177],"\u2208":[157],"computes":[159],"(sparse)":[161],"H":[163],"from":[164],"fixed":[166,182],"2":[174],"such":[175],"=":[178],"I(H)":[179],"interpretation":[183],"I.":[184],"To":[185],"best":[187],"knowledge,":[190],"first":[194],"\"interpretation":[196],"reversal\"":[197],"result":[198,202,213],"generalizes":[200],"Gajarsk\u00fd":[204],"et":[205],"al.":[206],"[LICS":[207],"2016],":[208],"who":[209],"showed":[210],"analogous":[212],"graphs":[221],"degree.":[224]},"counts_by_year":[],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2024-05-02T00:00:00"}