{"id":"https://openalex.org/W2143513910","doi":"https://doi.org/10.1137/110856186","title":"Total Acquisition in Graphs","display_name":"Total Acquisition in Graphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2143513910","doi":"https://doi.org/10.1137/110856186","mag":"2143513910"},"language":"en","primary_location":{"id":"doi:10.1137/110856186","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110856186","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5071250953","display_name":"Timothy D. LeSaulnier","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Timothy D. LeSaulnier","raw_affiliation_strings":["University of Illinois at Urbana Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074453237","display_name":"Noah Prince","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116845","display_name":"Illinois Mathematics and Science Academy","ror":"https://ror.org/024xf4148","country_code":"US","type":"education","lineage":["https://openalex.org/I4210116845"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Noah Prince","raw_affiliation_strings":["Illinois Mathematics and Science Academy"],"affiliations":[{"raw_affiliation_string":"Illinois Mathematics and Science Academy","institution_ids":["https://openalex.org/I4210116845"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083951311","display_name":"Paul S. Wenger","orcid":null},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul S. Wenger","raw_affiliation_strings":["University of Colorado, Denver"],"affiliations":[{"raw_affiliation_string":"University of Colorado, Denver","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017595199","display_name":"Douglas B. West","orcid":"https://orcid.org/0000-0001-8818-1667"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Douglas B. West","raw_affiliation_strings":["University of Illinois at Urbana Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049287396","display_name":"Pratik Worah","orcid":"https://orcid.org/0000-0002-2739-1246"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pratik Worah","raw_affiliation_strings":["University-of Chicago"],"affiliations":[{"raw_affiliation_string":"University-of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5071250953"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":2.2212,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.88454606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"4","first_page":"1800","last_page":"1819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9986000061035156,"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/T12288","display_name":"Optimization and Search Problems","score":0.9927999973297119,"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/combinatorics","display_name":"Combinatorics","score":0.9086621999740601},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7766183018684387},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7105835676193237},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6940712332725525},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5539572834968567},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4964466691017151},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.44032496213912964},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3393002152442932}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9086621999740601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7766183018684387},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7105835676193237},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6940712332725525},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5539572834968567},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4964466691017151},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.44032496213912964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3393002152442932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110856186","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110856186","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.imsa.edu:math_pr-1006","is_oa":false,"landing_page_url":"https://digitalcommons.imsa.edu/math_pr/7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196676","display_name":"DigitalCommons-IMSA (Illinois Mathematics and Science Academy)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116845","host_organization_name":"Illinois Mathematics and Science Academy","host_organization_lineage":["https://openalex.org/I4210116845"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications & Research","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.299.6739","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.6739","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~west/pubs/acqtot.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5346758441","display_name":null,"funder_award_id":"H98230-10-0363","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G7845798442","display_name":null,"funder_award_id":"H98230","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"}],"funders":[{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1975401569","https://openalex.org/W1978218692","https://openalex.org/W1981159511","https://openalex.org/W1983155670","https://openalex.org/W2029770599","https://openalex.org/W2035089435","https://openalex.org/W2399301123"],"related_works":["https://openalex.org/W1565889796","https://openalex.org/W2470039556","https://openalex.org/W4290190164","https://openalex.org/W4315607660","https://openalex.org/W4286851273","https://openalex.org/W2057668757","https://openalex.org/W2383129606","https://openalex.org/W1965411570","https://openalex.org/W4299272005","https://openalex.org/W2921294556"],"abstract_inverted_index":{"Let":[0],"$G$":[1,147,165],"be":[2],"a":[3,23,27,73,158],"weighted":[4],"graph":[5,186],"in":[6,136],"which":[7,131],"each":[8],"vertex":[9,24,29],"initially":[10],"has":[11,148,166],"weight":[12,21,39,49,71],"$1$.":[13],"A":[14],"total":[15,76],"acquisition":[16,54,77,128,177],"move":[17,37],"transfers":[18],"all":[19],"the":[20,32,36,38,48,61,65],"from":[22],"$u$":[25],"to":[26],"neighboring":[28],"$v$,":[30],"under":[31,218],"condition":[33],"that":[34],"before":[35],"on":[40,50,139],"$v$":[41],"is":[42,60,84,90,101,113],"at":[43],"least":[44],"as":[45,47],"large":[46],"$u$.":[51],"The":[52,88],"(total)":[53],"number":[55,129,178],"of":[56,64,67,75,183],"$G$,":[57],"written":[58],"$a_{t}(G)$,":[59],"minimum":[62],"size":[63],"set":[66],"vertices":[68],"with":[69,95,105,117,127,176,201],"positive":[70],"after":[72],"sequence":[74],"moves.":[78],"Among":[79],"connected":[80],"$n$-vertex":[81,185,199],"graphs,":[82],"$a_{t}(G)$":[83],"maximized":[85],"by":[86,190,208],"trees.":[87,140],"maximum":[89],"$\\Theta(\\sqrt{n\\lg":[91],"n})$":[92],"for":[93,103,115,173],"trees":[94,104,116,126],"diameter":[96,106,118,149,167],"$4$":[97],"or":[98],"$5$.":[99],"It":[100],"$\\left\\lfloor{(n+1)/3}\\right\\rfloor$":[102],"between":[107],"$6$":[108],"and":[109,111,169],"$\\frac23(n+1)$,":[110],"it":[112,207],"$\\left\\lceil{(2n-1-D)/4}\\right\\rceil$":[114],"$D$":[119],"when":[120,164],"$\\frac{2}{3}(n+1)\\le":[121],"D\\le":[122],"n-1$.":[123],"We":[124,212],"characterize":[125],"1,":[130],"permits":[132],"testing":[133],"$a_{t}(G)\\le":[134,152],"k$":[135],"time":[137],"$O(n^{k+2})$":[138],"If":[141,146],"$G\\ne":[142],"C_5$,":[143],"then":[144,151],"$\\min\\{a_{t}(G),a_{t}(\\overline{G})\\}=1$.":[145],"$2$,":[150],"32\\ln":[153],"n\\ln\\ln":[154],"n$;":[155],"we":[156,196],"conjecture":[157],"constant":[159],"upper":[160,216],"bound.":[161],"Indeed,":[162],"$a_{t}(G)=1$":[163],"$2$":[168],"no":[170],"$4$-cycle,":[171],"except":[172],"four":[174],"graphs":[175],"$2$.":[179],"Deleting":[180],"one":[181],"edge":[182,203],"an":[184,198,202],"cannot":[187],"increase":[188],"$a_{t}$":[189],"more":[191,209],"than":[192,210],"$6.84\\sqrt":[193],"n$,":[194],"but":[195],"construct":[197],"tree":[200],"whose":[204],"deletion":[205],"increases":[206],"$\\frac12\\sqrt{n}$.":[211],"also":[213],"obtain":[214],"multiplicative":[215],"bounds":[217],"products.":[219]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
