{"id":"https://openalex.org/W7160218340","doi":"https://doi.org/10.48550/arxiv.2605.00603","title":"Upward-Planar Drawings with Bounded Span","display_name":"Upward-Planar Drawings with Bounded Span","publication_year":2026,"publication_date":"2026-05-01","ids":{"openalex":"https://openalex.org/W7160218340","doi":"https://doi.org/10.48550/arxiv.2605.00603"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.00603","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00603","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.2605.00603","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010111302","display_name":"Patrizio Angelini","orcid":"https://orcid.org/0000-0002-7602-1524"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angelini, Patrizio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060809068","display_name":"Sabine Cornelsen","orcid":"https://orcid.org/0000-0002-1688-394X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cornelsen, Sabine","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006893407","display_name":"Giordano Da Lozzo","orcid":"https://orcid.org/0000-0003-2396-5174"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Da Lozzo, Giordano","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135123258","display_name":"Fabrizio Frati","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frati, Fabrizio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135163052","display_name":"Philipp Kindermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kindermann, Philipp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135212275","display_name":"Ignaz Rutter","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rutter, Ignaz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135200137","display_name":"Johannes Zink","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zink, Johannes","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":0.9760000109672546,"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":0.9760000109672546,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.00419999985024333,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.0026000000070780516,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/span","display_name":"Span (engineering)","score":0.6180999875068665},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5343000292778015},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4422000050544739},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.43160000443458557},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.41760000586509705},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4025999903678894},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3889000117778778},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.38600000739097595}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7318999767303467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6646000146865845},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.6180999875068665},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45500001311302185},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4422000050544739},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.41760000586509705},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.38600000739097595},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.3555999994277954},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.3312000036239624},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3248000144958496},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C17762858","wikidata":"https://www.wikidata.org/wiki/Q594001","display_name":"Edge cover","level":3,"score":0.3174000084400177},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.265500009059906},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.00603","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00603","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.2605.00603","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00603","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":[0,84],"consider":[1],"upward-planar":[2,73,82,93,133,170],"layered":[3],"drawings":[4,10],"of":[5,32,39,53,59,66,71,88,92,115,127,131,159],"directed":[6,116,139],"graphs,":[7],"i.e.,":[8],"crossing-free":[9],"in":[11,42],"which":[12],"each":[13],"edge":[14,41],"is":[15,46,62,75,135,172,180],"drawn":[16],"as":[17],"a":[18,44,156],"y-monotone":[19],"curve":[20],"going":[21],"upward":[22],"from":[23],"its":[24,27,54,81],"tail":[25],"to":[26,185],"head,":[28],"and":[29,56,95,99,109,141,164,190],"the":[30,33,47,51,57,60,63,76,86,90,103,113,119,125,129,167,178,186,191,194],"y-coordinates":[31,52],"vertices":[34],"are":[35],"integers.":[36],"The":[37,69],"span":[38,58,65,70,78,91,114,130],"an":[40,72,132],"such":[43],"drawing":[45,61],"absolute":[48],"difference":[49],"between":[50],"endpoints,":[55],"maximum":[64],"any":[67],"edge.":[68],"graph":[74,134,153],"minimum":[77],"over":[79],"all":[80],"drawings.":[83],"study":[85],"problem":[87,126,179],"determining":[89,128],"graphs":[94,163,165],"provide":[96],"both":[97],"combinatorial":[98,104],"algorithmic":[100,120],"results.":[101],"On":[102,118],"side,":[105,121],"we":[106,122,147,175],"present":[107],"upper":[108],"lower":[110],"bounds":[111],"for":[112,138,142,151],"trees.":[117],"show":[123,176],"that":[124,177],"NP-complete":[136],"already":[137],"trees":[140],"biconnected":[143],"single-source":[144],"graphs.":[145],"Moreover,":[146],"give":[148],"efficient":[149],"algorithms":[150],"several":[152],"families":[154],"with":[155,183],"bounded":[157],"number":[158,189],"sources,":[160],"including":[161],"st-planar":[162],"where":[166],"planar":[168],"or":[169],"embedding":[171],"prescribed.":[173],"Furthermore,":[174],"fixed-parameter":[181],"tractable":[182],"respect":[184],"vertex":[187],"cover":[188],"treedepth":[192],"plus":[193],"span.":[195]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-05T00:00:00"}
