{"id":"https://openalex.org/W7151962256","doi":"https://doi.org/10.48550/arxiv.2604.05786","title":"Realizing Planar Linkages in Polygonal Domains","display_name":"Realizing Planar Linkages in Polygonal Domains","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7151962256","doi":"https://doi.org/10.48550/arxiv.2604.05786"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.05786","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05786","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.2604.05786","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133231438","display_name":"Thomas Depian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Depian, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038474666","display_name":"Carolina Haase","orcid":"https://orcid.org/0000-0001-6696-074X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haase, Carolina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071390048","display_name":"Martin N\u00f6llenburg","orcid":"https://orcid.org/0000-0003-0454-3937"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N\u00f6llenburg, Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133148570","display_name":"Andr\u00e9 Schulz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schulz, Andr\u00e9","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":1,"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":0.6328999996185303,"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":0.6328999996185303,"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/T11870","display_name":"Structural Analysis and Optimization","score":0.2522999942302704,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.017100000753998756,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/embedding","display_name":"Embedding","score":0.6748999953269958},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6195999979972839},{"id":"https://openalex.org/keywords/polygonal-chain","display_name":"Polygonal chain","score":0.6137999892234802},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5806000232696533},{"id":"https://openalex.org/keywords/linkage","display_name":"Linkage (software)","score":0.5393000245094299},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5156999826431274},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5080999732017517},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45190000534057617},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4505000114440918}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6748999953269958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6288999915122986},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6195999979972839},{"id":"https://openalex.org/C182860218","wikidata":"https://www.wikidata.org/wiki/Q633674","display_name":"Polygonal chain","level":3,"score":0.6137999892234802},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5806000232696533},{"id":"https://openalex.org/C31266012","wikidata":"https://www.wikidata.org/wiki/Q6554340","display_name":"Linkage (software)","level":3,"score":0.5393000245094299},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5080999732017517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4999000132083893},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45190000534057617},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4505000114440918},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.36890000104904175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.36239999532699585},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.35409998893737793},{"id":"https://openalex.org/C103257674","wikidata":"https://www.wikidata.org/wiki/Q6934937","display_name":"Multiple edges","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3095000088214874},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.2874000072479248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2786000072956085},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.2567000091075897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.05786","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05786","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.2604.05786","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05786","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":{"A":[0],"linkage":[1],"$\\mathcal{L}$":[2,15,51],"consists":[3],"of":[4,50,62,81,100,136],"a":[5,20,47,121,147],"graph":[6],"$G=(V,E)$":[7],"and":[8,93,107,126,129,145,159],"an":[9,73],"edge-length":[10],"function":[11],"$\\ell$.":[12],"Deciding":[13],"whether":[14],"can":[16],"be":[17,85],"realized":[18],"as":[19],"planar":[21],"straight-line":[22],"embedding":[23],"in":[24,87,143],"$\\mathbb{R}^2$":[25],"with":[26,95,123],"edge":[27],"length":[28],"$\\ell(e)$":[29],"for":[30,66,150],"all":[31],"$e":[32],"\\in":[33],"E$":[34],"is":[35,52,120,161],"$\\exists\\mathbb{R}$-complete":[36],"[Abel":[37],"et":[38],"al.,":[39],"JoCG'25],":[40],"even":[41,102],"if":[42,103,153],"$\\ell":[43,104,130],"\\equiv":[44,105,131],"1$,":[45],"but":[46],"considerable":[48],"part":[49],"rigid.":[53],"In":[54],"this":[55],"paper,":[56],"we":[57,114,140],"study":[58],"the":[59,63,79,88,98,116,134],"computational":[60],"complexity":[61],"realization":[64],"question":[65],"structurally":[67],"simpler,":[68],"less":[69],"rigid":[70,138],"linkages":[71],"inside":[72],"open":[74],"polygonal":[75],"domain":[76],"$P$,":[77],"where":[78,118],"placement":[80],"some":[82],"vertices":[83],"may":[84],"specified":[86],"input.":[89],"We":[90],"show":[91],"XP-membership":[92],"W[1]-hardness":[94],"respect":[96],"to":[97],"size":[99],"$G$,":[101],"1$":[106],"no":[108],"vertex":[109],"positions":[110],"are":[111],"prescribed.":[112],"Furthermore,":[113],"consider":[115],"case":[117],"$G$":[119,154],"path":[122],"prescribed":[124],"start":[125],"end":[127],"position":[128],"1$.":[132],"Despite":[133],"absence":[135],"any":[137],"components,":[139],"obtain":[141],"NP-hardness":[142],"general,":[144],"provide":[146],"linear-time":[148],"algorithm":[149],"arbitrary":[151],"$\\ell$":[152],"has":[155],"only":[156],"three":[157],"edges":[158],"$P$":[160],"convex.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-09T00:00:00"}