{"id":"https://openalex.org/W7162552134","doi":"https://doi.org/10.4230/lipics.socg.2026.36","title":"Upward Book Embeddings of Partitioned Digraphs","display_name":"Upward Book Embeddings of Partitioned Digraphs","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162552134","doi":"https://doi.org/10.4230/lipics.socg.2026.36"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25842","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.36/LIPIcs.SoCG.2026.36.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":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.36/LIPIcs.SoCG.2026.36.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006893407","display_name":"Giordano Da Lozzo","orcid":"https://orcid.org/0000-0003-2396-5174"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Da Lozzo, Giordano","raw_affiliation_strings":["ICITA Department, Roma Tre University, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2396-5174","affiliations":[{"raw_affiliation_string":"ICITA Department, Roma Tre University, Italy","institution_ids":["https://openalex.org/I119003972"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025842302","display_name":"Fabrizio Frati","orcid":"https://orcid.org/0000-0001-5987-8713"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Frati, Fabrizio","raw_affiliation_strings":["ICITA Department, Roma Tre University, Italy"],"raw_orcid":"https://orcid.org/0000-0001-5987-8713","affiliations":[{"raw_affiliation_string":"ICITA Department, Roma Tre University, Italy","institution_ids":["https://openalex.org/I119003972"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137180350","display_name":"Ignaz Rutter","orcid":"https://orcid.org/0000-0002-3794-4406"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rutter, Ignaz","raw_affiliation_strings":["Faculty of Computer Science and Mathematics, University of Passau, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3794-4406","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Mathematics, University of Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.68924085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.5317999720573425,"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":0.5317999720573425,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.13660000264644623,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.12520000338554382,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/digraph","display_name":"Digraph","score":0.9136999845504761},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.8644000291824341},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5745999813079834},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4869000017642975},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47450000047683716},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.44190001487731934},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41990000009536743},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.3977000117301941}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9136999845504761},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.8644000291824341},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6965000033378601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.642300009727478},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5745999813079834},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4869000017642975},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47839999198913574},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47450000047683716},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41990000009536743},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C35435516","wikidata":"https://www.wikidata.org/wiki/Q5370016","display_name":"Embedding problem","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.28679999709129333},{"id":"https://openalex.org/C103257674","wikidata":"https://www.wikidata.org/wiki/Q6934937","display_name":"Multiple edges","level":3,"score":0.2825999855995178},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25842","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.36/LIPIcs.SoCG.2026.36.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.2026.36","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.36","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"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:25842","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.36/LIPIcs.SoCG.2026.36.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/W7162552134.pdf","grobid_xml":"https://content.openalex.org/works/W7162552134.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,95,149],"1999,":[1],"Heath,":[2],"Pemmaraju,":[3],"and":[4,40,100,131,136,160,197],"Trenk":[5],"[SIAM":[6,102],"J.":[7,103],"Comput.":[8,104],"28(4),":[9],"1999]":[10,106],"extended":[11],"the":[12,21,29,34,41,53,92,109,113,142,163,178,203,207,213,223,227,243,252,266],"classic":[13],"notion":[14],"of":[15,23,111,115,120,157,177,202,206,245,269],"book":[16,25,80,118,155,185,248],"embeddings":[17,156,180],"to":[18,84,87],"digraphs,":[19],"introducing":[20],"concept":[22],"upward":[24,79,117,154,179,184,247],"embeddings,":[26],"in":[27,36,52,187,194,259],"which":[28],"vertices":[30],"must":[31],"appear":[32],"along":[33],"spine":[35],"a":[37,58,68,96,121,174,199,239,277],"topological":[38],"order":[39],"edges":[42,51,86],"are":[43],"partitioned":[44,59,74,122,158,236],"into":[45,75,272],"pages,":[46],"so":[47],"that":[48,66,108,181,212,250],"no":[49],"two":[50,188],"same":[54],"page":[55],"cross.":[56],"For":[57],"digraph":[60,69,123,237],"G":[61],"=":[62,129,167,219],"(V,":[63],"\u22c3^k_{i=1}":[64],"E_i),":[65],"is,":[67],"whose":[70],"edge":[71],"set":[72],"is":[73,82,124,173],"k":[76,128,146,166,218],"subsets,":[77],"an":[78,116,183,234,246],"embedding":[81,119,186,249,255],"required":[83],"assign":[85],"pages":[88],"as":[89],"prescribed":[90,240],"by":[91],"given":[93,253],"partition.":[94],"companion":[97],"paper,":[98,151],"Heath":[99],"Pemmaraju":[101],"28(5),":[105],"proved":[107],"problem":[110,143,214],"testing":[112,279],"existence":[114,244],"linear-time":[125],"solvable":[126],"for":[127,145,226,233,281],"1":[130],"recently":[132],"Akitaya,":[133],"Demaine,":[134],"Hesterberg,":[135],"Liu":[137],"[GD,":[138],"2017]":[139],"have":[140],"shown":[141],"NP-complete":[144,216],"\u2265":[147],"3.":[148],"this":[150,192],"we":[152,210,230,275],"study":[153],"digraphs":[159],"focus":[161],"on":[162],"unsolved":[164],"case":[165],"2.":[168],"Our":[169],"first":[170],"main":[171],"result":[172],"novel":[175],"characterization":[176,193],"support":[182],"pages.":[189],"We":[190],"exploit":[191],"several":[195],"ways,":[196],"obtain":[198],"rich":[200],"picture":[201],"complexity":[204,224],"landscape":[205],"problem.":[208,228],"First,":[209],"show":[211,231],"remains":[215],"when":[217],"2,":[220],"thus":[221],"closing":[222],"gap":[225],"Second,":[229],"that,":[232],"n-vertex":[235],"with":[238],"planar":[241,254],"embedding,":[242],"respects":[251],"can":[256],"be":[257],"tested":[258],"O(n":[260],"log\u00b3":[261],"n)":[262],"time.":[263],"Finally,":[264],"leveraging":[265],"SPQ(R)-tree":[267],"decomposition":[268],"biconnected":[270,282],"graphs":[271],"triconnected":[273],"components,":[274],"present":[276],"cubic-time":[278],"algorithm":[280],"directed":[283],"partial":[284],"2-trees.":[285]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-05-28T00:00:00"}