{"id":"https://openalex.org/W1973784010","doi":"https://doi.org/10.1145/1921659.1921660","title":"Data structures for mergeable trees","display_name":"Data structures for mergeable trees","publication_year":2011,"publication_date":"2011-03-01","ids":{"openalex":"https://openalex.org/W1973784010","doi":"https://doi.org/10.1145/1921659.1921660","mag":"1973784010"},"language":"en","primary_location":{"id":"doi:10.1145/1921659.1921660","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1921659.1921660","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024478433","display_name":"Loukas Georgiadis","orcid":"https://orcid.org/0000-0002-9706-7409"},"institutions":[{"id":"https://openalex.org/I89506807","display_name":"University of Western Macedonia","ror":"https://ror.org/00a5pe906","country_code":"GR","type":"education","lineage":["https://openalex.org/I89506807"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Loukas Georgiadis","raw_affiliation_strings":["University of Western Macedonia, Kozani, Greece","University of Western Macedonia Kozani, Greece#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Macedonia, Kozani, Greece","institution_ids":["https://openalex.org/I89506807"]},{"raw_affiliation_string":"University of Western Macedonia Kozani, Greece#TAB#","institution_ids":["https://openalex.org/I89506807"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006699796","display_name":"Haim Kaplan","orcid":"https://orcid.org/0000-0001-9586-8002"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Haim Kaplan","raw_affiliation_strings":["Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067943969","display_name":"Nira Shafrir","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Nira Shafrir","raw_affiliation_strings":["Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051027549","display_name":"Robert E. Tarjan","orcid":"https://orcid.org/0000-0001-7505-5768"},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]},{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert E. Tarjan","raw_affiliation_strings":["Princeton University, Princeton, NJ and Hewlett-Packard Laboratories, Palo Alto, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ and Hewlett-Packard Laboratories, Palo Alto, CA","institution_ids":["https://openalex.org/I1324840837","https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063407134","display_name":"Renato F. Werneck","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Renato F. Werneck","raw_affiliation_strings":["Microsoft Research, La Avenida, Moutain View, CA","Microsoft Research, La Avenida, Moutain View, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, La Avenida, Moutain View, CA","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"Microsoft Research, La Avenida, Moutain View, CA#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5024478433"],"corresponding_institution_ids":["https://openalex.org/I89506807"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.06990881,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"7","issue":"2","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9997000098228455,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9997000098228455,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/amortized-analysis","display_name":"Amortized analysis","score":0.8204081058502197},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.6296400427818298},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5998092889785767},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5612622499465942},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5309972763061523},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5132946372032166},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.5017523765563965},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.48711204528808594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44137272238731384},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4207099974155426},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4128798842430115},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3874639868736267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38551607728004456},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.08323514461517334}],"concepts":[{"id":"https://openalex.org/C142417499","wikidata":"https://www.wikidata.org/wiki/Q331716","display_name":"Amortized analysis","level":3,"score":0.8204081058502197},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.6296400427818298},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5998092889785767},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5612622499465942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5309972763061523},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5132946372032166},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.5017523765563965},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.48711204528808594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44137272238731384},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4207099974155426},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4128798842430115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3874639868736267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38551607728004456},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.08323514461517334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1921659.1921660","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1921659.1921660","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.9637","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.9637","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0711.1682v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6800000071525574}],"awards":[{"id":"https://openalex.org/G3751712049","display_name":null,"funder_award_id":"975/06","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G555557140","display_name":null,"funder_award_id":"2006204","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G5697371125","display_name":null,"funder_award_id":"112-0188-1234-12CCF-0830676CCF-0832797","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1481686123","https://openalex.org/W1963524245","https://openalex.org/W1964669678","https://openalex.org/W1971842242","https://openalex.org/W1972748018","https://openalex.org/W1977155699","https://openalex.org/W1986022261","https://openalex.org/W1987927249","https://openalex.org/W1990488650","https://openalex.org/W1991146548","https://openalex.org/W2018777660","https://openalex.org/W2018804864","https://openalex.org/W2019724649","https://openalex.org/W2021615496","https://openalex.org/W2025791989","https://openalex.org/W2037658490","https://openalex.org/W2054014036","https://openalex.org/W2061634390","https://openalex.org/W2065209187","https://openalex.org/W2089016801","https://openalex.org/W2093012474","https://openalex.org/W2121473031","https://openalex.org/W2130055503","https://openalex.org/W4389615669"],"related_works":["https://openalex.org/W8290509","https://openalex.org/W2184537587","https://openalex.org/W2065411828","https://openalex.org/W2374253787","https://openalex.org/W3092127654","https://openalex.org/W1482484961","https://openalex.org/W4246145339","https://openalex.org/W2076407808","https://openalex.org/W2006811735","https://openalex.org/W2018777660"],"abstract_inverted_index":{"Motivated":[0],"by":[1,262],"an":[2,27,109,184],"application":[3],"in":[4,40,146,150,178,202,213,256,266],"computational":[5],"geometry,":[6],"we":[7,69,159,223],"consider":[8],"a":[9,18,42,60,85,161,179,225,233,241],"novel":[10],"variant":[11,25],"of":[12,15,20,63,67,87,96,181,244,270,282],"the":[13,37,93,125,136,141,147,210,257,264,267],"problem":[14],"efficiently":[16],"maintaining":[17],"forest":[19,112],"dynamic":[21,116,230,246,283],"rooted":[22],"trees.":[23,284],"This":[24,174,249],"includes":[26],"operation":[28,44,118,239],"that":[29,74,144,163,227],"merges":[30],"two":[31],"tree":[32,117,207,238,247],"paths.":[33,97],"In":[34,65],"contrast":[35],"to":[36,59],"standard":[38,115,229,245],"problem,":[39],"which":[41,151,214],"single":[43],"can":[45,54,199,252],"only":[46,76,261],"add":[47,55],"or":[48,132],"delete":[49,57],"one":[50,52],"arc,":[51],"merge":[53,99],"and":[56,89,113,219,278],"up":[58],"linear":[61],"number":[62,243],"arcs.":[64],"spite":[66],"this,":[68],"develop":[70],"three":[71,272],"different":[72,275,280],"methods":[73,273],"need":[75],"polylogarithmic":[77],"time":[78,107,169],"per":[79,170],"operation.":[80],"The":[81],"first":[82],"method":[83,162,226,251],"extends":[84],"solution":[86],"Farach":[88],"Thorup":[90],"[1998]":[91],"for":[92,192],"special":[94,142],"case":[95,143,212],"Each":[98,269],"takes":[100,119,164],"O":[101,120,165,203],"(log":[102,121,166],"2":[103],"n":[104,110,122,167,186,188,194,205],")":[105,123,168,189,206],"amortized":[106],"on":[108,135],"-node":[111],"each":[114,236],"time;":[124],"latter":[126],"bound":[127,191],"is":[128,175],"amortized,":[129],"worst":[130],"case,":[131],"randomized":[133],"depending":[134],"underlying":[137],"data":[138],"structure.":[139],"For":[140,209],"occurs":[145],"motivating":[148,258],"application,":[149,259],"arbitrary":[152],"arc":[153],"deletions":[154],"(cuts)":[155],"do":[156],"not":[157],"occur,":[158],"give":[160,224],"operation,":[171],"including":[172],"merging.":[173],"best":[176],"possible":[177],"model":[180],"computation":[182],"with":[183],"\u03a9(":[185],"log":[187],"lower":[190],"sorting":[193,198],"numbers,":[195],"since":[196],"such":[197],"be":[200,254],"done":[201],"(":[204],"operations.":[208,248],"even-more-special":[211],"there":[215],"are":[216],"no":[217,220],"cuts":[218],"parent":[221],"queries,":[222],"uses":[228],"trees":[231],"as":[232],"black":[234],"box:":[235],"mergeable":[237],"becomes":[240],"constant":[242],"third":[250],"also":[253],"used":[255],"but":[260],"changing":[263],"algorithm":[265],"application.":[268],"our":[271],"needs":[274],"analytical":[276],"tools":[277],"reveals":[279],"properties":[281]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
