{"id":"https://openalex.org/W7161769259","doi":"https://doi.org/10.48550/arxiv.2605.19962","title":"Computing the Arc-Deletion Distance to Orchard Networks is NP-hard","display_name":"Computing the Arc-Deletion Distance to Orchard Networks is NP-hard","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161769259","doi":"https://doi.org/10.48550/arxiv.2605.19962"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.19962","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19962","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2605.19962","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136569526","display_name":"Peng Li","orcid":"https://orcid.org/0000-0002-6509-1076"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Peng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136543226","display_name":"Zhiwei Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zhiwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045775770","display_name":"Yangjing Long","orcid":"https://orcid.org/0000-0001-5934-1326"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Long, Yangjing","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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.5529000163078308,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.5529000163078308,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.4336000084877014,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.0038999998942017555,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/phylogenetic-tree","display_name":"Phylogenetic tree","score":0.8557000160217285},{"id":"https://openalex.org/keywords/phylogenetic-network","display_name":"Phylogenetic network","score":0.840399980545044},{"id":"https://openalex.org/keywords/reticulate","display_name":"Reticulate","score":0.8384000062942505},{"id":"https://openalex.org/keywords/reticulate-evolution","display_name":"Reticulate evolution","score":0.6204000115394592},{"id":"https://openalex.org/keywords/computational-phylogenetics","display_name":"Computational phylogenetics","score":0.5600000023841858},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5167999863624573},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.489300012588501},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.3905999958515167}],"concepts":[{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.8557000160217285},{"id":"https://openalex.org/C26619641","wikidata":"https://www.wikidata.org/wiki/Q3142246","display_name":"Phylogenetic network","level":4,"score":0.840399980545044},{"id":"https://openalex.org/C2780432395","wikidata":"https://www.wikidata.org/wiki/Q21149008","display_name":"Reticulate","level":2,"score":0.8384000062942505},{"id":"https://openalex.org/C2778727739","wikidata":"https://www.wikidata.org/wiki/Q18434417","display_name":"Reticulate evolution","level":4,"score":0.6204000115394592},{"id":"https://openalex.org/C41168302","wikidata":"https://www.wikidata.org/wiki/Q3772859","display_name":"Computational phylogenetics","level":5,"score":0.5600000023841858},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5167999863624573},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.489300012588501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4578999876976013},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41830000281333923},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C2780753983","wikidata":"https://www.wikidata.org/wiki/Q236371","display_name":"Orchard","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C90132467","wikidata":"https://www.wikidata.org/wiki/Q171184","display_name":"Phylogenetics","level":3,"score":0.3368000090122223},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30869999527931213},{"id":"https://openalex.org/C55919133","wikidata":"https://www.wikidata.org/wiki/Q7644297","display_name":"Supertree","level":4,"score":0.29980000853538513},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2989000082015991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2946999967098236},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.28630000352859497},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2694000005722046},{"id":"https://openalex.org/C53208351","wikidata":"https://www.wikidata.org/wiki/Q7837630","display_name":"Tree rearrangement","level":4,"score":0.2660999894142151},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.25040000677108765},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.19962","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19962","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":"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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.19962","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19962","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"Phylogenetic":[0],"networks":[1,25],"generalize":[2],"phylogenetic":[3,22,60,101],"trees":[4],"by":[5],"allowing":[6],"reticulate":[7,54],"evolutionary":[8],"events":[9],"such":[10],"as":[11,49],"horizontal":[12],"gene":[13],"transfer":[14],"and":[15,34,94],"hybridization.":[16],"Among":[17],"the":[18,42,50,79,87,97],"many":[19],"subclasses":[20],"of":[21,53,90,100],"networks,":[23,47],"orchard":[24,46,64],"have":[26],"attracted":[27],"increasing":[28],"attention":[29],"due":[30],"to":[31,45,96],"their":[32],"structural":[33],"algorithmic":[35],"properties.":[36],"In":[37],"this":[38,70,91],"paper,":[39],"we":[40],"study":[41],"arc-deletion":[43],"distance":[44,71],"defined":[48],"minimum":[51],"number":[52],"arcs":[55],"whose":[56],"deletion":[57],"transforms":[58],"a":[59,75],"network":[61,102],"into":[62],"an":[63],"network.":[65],"We":[66],"prove":[67],"that":[68],"computing":[69],"is":[72],"NP-hard":[73],"via":[74],"polynomial-time":[76],"reduction":[77],"from":[78],"Degree-3":[80],"Vertex":[81],"Cover":[82],"problem.":[83],"Our":[84],"result":[85],"establishes":[86],"computational":[88],"intractability":[89],"proximity":[92],"measure":[93],"contributes":[95],"complexity":[98],"theory":[99],"transformations.":[103]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-21T00:00:00"}
