{"id":"https://openalex.org/W7140168530","doi":"https://doi.org/10.48550/arxiv.2603.22262","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":"2026-03-23","ids":{"openalex":"https://openalex.org/W7140168530","doi":"https://doi.org/10.48550/arxiv.2603.22262"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.22262","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22262","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.22262","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bjerkevik, H\u00e5vard Bakke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bjerkevik, H\u00e5vard Bakke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Dorfer, Joseph","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dorfer, Joseph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Kleist, Linda","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kleist, Linda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ueckerdt, Torsten","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ueckerdt, Torsten","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Vogtenhuber, Birgit","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vogtenhuber, Birgit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.8440999984741211,"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":0.8440999984741211,"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":0.03280000016093254,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.013799999840557575,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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":0.7634999752044678},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.590499997138977},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.578000009059906},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5322999954223633},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5185999870300293},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.49309998750686646},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4397999942302704},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.40540000796318054},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.37439998984336853}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.7634999752044678},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.741100013256073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5952000021934509},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.590499997138977},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.578000009059906},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5322999954223633},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5185999870300293},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4397999942302704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4311000108718872},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.3513999879360199},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.32679998874664307},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C2992444157","wikidata":"https://www.wikidata.org/wiki/Q775079","display_name":"Single point","level":3,"score":0.29809999465942383},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.2888000011444092},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C23394520","wikidata":"https://www.wikidata.org/wiki/Q4919350","display_name":"Shortest-path tree","level":3,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.22262","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22262","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.22262","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22262","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":"Preprint"},"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":{"We":[0,255],"consider":[1],"the":[2,23,25,55,106,116,121,126,138,168,186,199,202,211,214,221,233,236,261,266,296,300,303],"problem":[3],"of":[4,16,57,80,140,223,235,248,251,260,284,302],"reconfiguring":[5],"non-crossing":[6,34,173],"spanning":[7,35,45,174],"trees":[8,46,175,262],"on":[9,37,72,232,244,299],"point":[10,180],"sets.":[11],"For":[12],"a":[13,30,58,245,274,281],"set":[14],"$P$":[15,38,79],"$n$":[17,81,308],"points":[18,82,309],"in":[19,22,83,182,310],"general":[20],"position":[21,312],"plane,":[24],"flip":[26,62,169,193,237,282,304],"graph":[27,63,305],"$F(P)$":[28,306],"has":[29,64],"vertex":[31],"for":[32,77,104,124,179,190,307],"each":[33,52],"tree":[36],"and":[39,97,108,143,201,208,213],"an":[40,70,218],"edge":[41,204,216],"between":[42,171],"any":[43,290],"two":[44,172],"that":[47,145,166,257,277],"can":[48],"be":[49,120],"transformed":[50],"into":[51],"other":[53,291],"by":[54],"exchange":[56],"single":[59],"edge.":[60],"This":[61],"been":[65],"intensively":[66],"studied,":[67],"lately":[68],"with":[69],"emphasis":[71],"determining":[73,125],"its":[74],"diameter":[75,127,234,301],"diam$(F(P))$":[76],"sets":[78,181],"convex":[84,183,311],"position.":[85,184],"The":[86,101],"current":[87],"best":[88],"bounds":[89],"are":[90,111],"$\\frac{14}{9}n-O(1)":[91],"\\leq$":[92],"diam$(F(P))<\\frac{15}{9}n-3$":[93],"[Bjerkevik,":[94],"Kleist,":[95],"Ueckerdt,":[96],"Vogtenhuber;":[98],"SODA":[99],"2025].":[100],"crucial":[102],"tool":[103,147],"both":[105],"upper":[107],"lower":[109,240,267,297],"bound":[110,241,268,298],"so-called":[112],"*conflict":[113],"graphs*,":[114],"which":[115,252],"authors":[117],"stated":[118],"might":[119],"key":[122],"ingredient":[123],"(up":[128],"to":[129,164,273,289,313],"lower-order":[130],"terms).":[131],"In":[132],"this":[133,146],"paper,":[134],"we":[135,160,228,294],"pick":[136],"up":[137,272],"concept":[139],"conflict":[141,162],"graphs":[142,163],"show":[144,165,256],"is":[148,176,242,253,263,269],"even":[149,178],"more":[150,191],"versatile":[151],"than":[152],"previously":[153],"hoped.":[154],"As":[155],"our":[156],"first":[157],"main":[158],"result,":[159],"use":[161],"computing":[167],"distance":[170],"NP-hard,":[177],"Interestingly,":[185],"result":[187],"still":[188],"holds":[189],"constrained":[192],"operations,":[194],"concretely,":[195],"compatible":[196],"flips":[197],"(where":[198,210],"removed":[200,212],"added":[203,215],"do":[205],"not":[206],"cross)":[207],"rotations":[209],"share":[217],"endpoint).":[219],"Extending":[220],"line":[222],"research":[224],"from":[225],"[BKUV":[226],"SODA25],":[227],"present":[229],"new":[230],"insights":[231],"graph.":[238],"Their":[239],"based":[243],"constant-size":[246],"pair":[247],"trees,":[249],"one":[250,259],"*stacked*.":[254],"if":[258],"stacked,":[264],"then":[265],"indeed":[270],"optimal":[271],"constant":[275],"term,":[276],"is,":[278],"there":[279],"exists":[280],"sequence":[283],"length":[285],"at":[286],"most":[287],"$\\frac{14}{9}(n-1)$":[288],"tree.":[292],"Lastly,":[293],"improve":[295],"$\\frac{11}{7}n-o(n)$.":[314]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-25T00:00:00"}