{"id":"https://openalex.org/W7162580303","doi":"https://doi.org/10.4230/lipics.socg.2026.16","title":"Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds","display_name":"Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162580303","doi":"https://doi.org/10.4230/lipics.socg.2026.16"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25822","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.16","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.16/LIPIcs.SoCG.2026.16.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":null,"raw_type":"InProceedings"},"type":"conference-paper","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.16/LIPIcs.SoCG.2026.16.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086819896","display_name":"H\u00e5vard Bakke Bjerkevik","orcid":"https://orcid.org/0000-0001-9778-0354"},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bjerkevik, H\u00e5vard Bakke","raw_affiliation_strings":["University at Albany, SUNY, NY, USA"],"raw_orcid":"https://orcid.org/0000-0001-9778-0354","affiliations":[{"raw_affiliation_string":"University at Albany, SUNY, NY, USA","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137119461","display_name":"Joseph Dorfer","orcid":"https://orcid.org/0009-0004-9276-7870"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Dorfer, Joseph","raw_affiliation_strings":["Graz University of Technology, Austria"],"raw_orcid":"https://orcid.org/0009-0004-9276-7870","affiliations":[{"raw_affiliation_string":"Graz University of Technology, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090048794","display_name":"Linda Kleist","orcid":"https://orcid.org/0000-0002-3786-916X"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kleist, Linda","raw_affiliation_strings":["University of Hamburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3786-916X","affiliations":[{"raw_affiliation_string":"University of Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063296115","display_name":"Torsten Ueckerdt","orcid":"https://orcid.org/0000-0002-0645-9715"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ueckerdt, Torsten","raw_affiliation_strings":["Karlsruhe Institute of Technology, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0645-9715","affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137097607","display_name":"Birgit Vogtenhuber","orcid":"https://orcid.org/0000-0002-7166-4467"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Vogtenhuber, Birgit","raw_affiliation_strings":["Graz University of Technology, Austria"],"raw_orcid":"https://orcid.org/0000-0002-7166-4467","affiliations":[{"raw_affiliation_string":"Graz University of Technology, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.7440999746322632,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.7440999746322632,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.05649999901652336,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.03660000115633011,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.7775999903678894},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.5924999713897705},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5371999740600586},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.534500002861023},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.527899980545044},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5263000130653381},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4652999937534332},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.3991999924182892}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.7775999903678894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7384999990463257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5979999899864197},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.5924999713897705},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5371999740600586},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.534500002861023},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.527899980545044},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5263000130653381},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4180999994277954},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3991999924182892},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.32600000500679016},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.32589998841285706},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C23394520","wikidata":"https://www.wikidata.org/wiki/Q4919350","display_name":"Shortest-path tree","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C2992444157","wikidata":"https://www.wikidata.org/wiki/Q775079","display_name":"Single point","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.2743000090122223},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.265500009059906},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25822","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.16","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.16/LIPIcs.SoCG.2026.16.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":null,"raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.socg.2026.16","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.16","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25822","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.16","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.16/LIPIcs.SoCG.2026.16.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":null,"raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162580303.pdf","grobid_xml":"https://content.openalex.org/works/W7162580303.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,288],"consider":[1],"the":[2,23,25,55,92,124,134,139,144,156,162,190,208,221,224,233,236,248,251,258,294,299,329,333,336],"problem":[3],"of":[4,16,57,83,158,250,260,274,277,280,293,317,335],"reconfiguring":[5],"non-crossing":[6,34,195],"spanning":[7,35,45,196],"trees":[8,46,197,295],"on":[9,37,75,247,270,332],"point":[10,202],"sets.":[11],"For":[12,89],"a":[13,30,58,62,108,271,281,307,314],"set":[14],"P":[15,38,82],"n":[17,84,341],"points":[18,85,342],"in":[19,22,86,107,204,343],"general":[20],"position":[21,345],"plane,":[24],"\ufb02ip":[26],"graph":[27,66,338],"\u2131(P)":[28,339],"has":[29,67],"vertex":[31],"for":[32,80,122,142,201,212,340],"each":[33,52],"tree":[36],"and":[39,115,126,165,223,230,235],"an":[40,73,240],"edge":[41,60,226,238],"between":[42,193],"any":[43,323],"two":[44,194],"that":[47,167,188,290,310],"can":[48],"be":[49,138],"transformed":[50],"into":[51],"other":[53,324],"by":[54,254],"exchange":[56],"single":[59],"(coined":[61],"flip).":[63],"This":[64],"flip":[65,191,215,252,315,337],"been":[68],"intensively":[69],"studied,":[70],"lately":[71],"with":[72],"emphasis":[74],"determining":[76,143],"its":[77],"diameter":[78,145,249,334],"diam(\u2131(P))":[79,101],"sets":[81,203],"convex":[87,205,344],"position.":[88,206],"this":[90,151,168,255],"case,":[91],"current":[93],"best":[94],"bounds":[95],"are":[96,129],"14/9\u22c5n":[97],"-":[98,104],"O(1)":[99],"\u2264":[100],"<":[102],"15/9\u22c5n":[103],"3,":[105],"obtained":[106],"recent":[109],"breakthrough":[110],"work":[111,164],"[Bjerkevik,":[112],"Kleist,":[113],"Ueckerdt,":[114],"Vogtenhuber;":[116],"SODA":[117],"2025].":[118],"The":[119],"crucial":[120],"tool":[121,169],"both":[123],"upper":[125],"lower":[127,266,300,330],"bound":[128,267,301,331],"so-called":[130],"conflict":[131,159,184],"graphs,":[132],"which":[133,278],"authors":[135],"stated":[136],"might":[137],"key":[140],"ingredient":[141],"(up":[146],"to":[147,186,285,306,322,346],"lower-order":[148],"terms).":[149],"In":[150],"paper,":[152],"we":[153,182,243,283,327],"pick":[154],"up":[155,305],"concept":[157],"graphs":[160,185],"from":[161,262],"above-mentioned":[163],"show":[166,187,289],"is":[170,198,268,279,296,302],"even":[171,200],"more":[172,213],"versatile":[173],"than":[174],"previously":[175],"hoped.":[176],"As":[177],"our":[178],"first":[179],"main":[180],"result,":[181],"use":[183],"computing":[189],"distance":[192],"NP-hard,":[199],"Interestingly,":[207],"result":[209],"still":[210],"holds":[211],"constrained":[214],"operations,":[216],"concretely,":[217],"compatible":[218],"flips":[219],"(where":[220,232],"removed":[222,234],"added":[225,237],"do":[227],"not":[228],"cross)":[229],"rotations":[231],"share":[239],"endpoint).":[241],"Additionally,":[242],"present":[244],"new":[245],"insights":[246],"graph,":[253],"directly":[256],"extending":[257],"line":[259],"research":[261],"[BKUV":[263],"SODA25].":[264],"Their":[265],"based":[269],"constant-size":[272],"pair":[273],"trees,":[275],"one":[276,292],"type":[282],"refer":[284],"as":[286],"stacked.":[287],"if":[291],"stacked,":[297],"then":[298],"indeed":[303],"optimal":[304],"constant":[308],"term,":[309],"is,":[311],"there":[312],"exists":[313],"sequence":[316],"length":[318],"at":[319],"most":[320],"14/9\u22c5(n-1)":[321],"tree.":[325],"Lastly,":[326],"improve":[328],"11/7\u22c5n-o(n).":[347]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-28T00:00:00"}