{"id":"https://openalex.org/W2104525387","doi":"https://doi.org/10.1137/s0895480103420744","title":"Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer","display_name":"Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2104525387","doi":"https://doi.org/10.1137/s0895480103420744","mag":"2104525387"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480103420744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480103420744","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cs/0212054","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ching-Chi Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ching-Chi Lin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Hsueh-I Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hsueh-I Lu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"I-Fan Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I-Fan Sun","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.106,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.9330855,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"18","issue":"1","first_page":"19","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9192000031471252,"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":0.9192000031471252,"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":0.03959999978542328,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.008100000210106373,"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/visibility","display_name":"Visibility","score":0.7908999919891357},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6381999850273132},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6195999979972839},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5436999797821045},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.5264999866485596},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.489300012588501},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4235999882221222},{"id":"https://openalex.org/keywords/visibility-graph","display_name":"Visibility graph","score":0.41519999504089355}],"concepts":[{"id":"https://openalex.org/C123403432","wikidata":"https://www.wikidata.org/wiki/Q654068","display_name":"Visibility","level":2,"score":0.7908999919891357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6577000021934509},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6381999850273132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6367999911308289},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6195999979972839},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5436999797821045},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C173362246","wikidata":"https://www.wikidata.org/wiki/Q8216024","display_name":"Visibility graph","level":3,"score":0.41519999504089355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4066999852657318},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.36910000443458557},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.33410000801086426},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30869999527931213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29350000619888306},{"id":"https://openalex.org/C114645060","wikidata":"https://www.wikidata.org/wiki/Q5431294","display_name":"Faithful representation","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26910001039505005},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895480103420744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480103420744","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cs/0212054","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0212054","pdf_url":"https://arxiv.org/pdf/cs/0212054","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cs/0212054","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0212054","pdf_url":"https://arxiv.org/pdf/cs/0212054","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1964716955","https://openalex.org/W1965372753","https://openalex.org/W1972622848","https://openalex.org/W2003525146","https://openalex.org/W2006382572","https://openalex.org/W2024208603","https://openalex.org/W2039512408","https://openalex.org/W2082205964","https://openalex.org/W2083176195","https://openalex.org/W2090387200","https://openalex.org/W2091252880","https://openalex.org/W2118697430","https://openalex.org/W2120892678","https://openalex.org/W2166735327","https://openalex.org/W4205163994"],"related_works":[],"abstract_inverted_index":{"Let":[0],"G":[1,16,35,89,95,147,160,170,178],"be":[2],"an":[3],"n-node":[4],"planar":[5],"graph.":[6],"In":[7,42],"a":[8,20,57,71,91,126,137,194,198,203],"visibility":[9,52,92,157,175],"representation":[10,53,93,158,176],"of":[11,15,34,54,60,78,94,121,189,205],"G,":[12,63],"each":[13,40],"node":[14],"is":[17,136,161,171,179],"represented":[18],"by":[19,115],"horizontal":[21],"line":[22,27],"segment":[23],"such":[24],"that":[25,76],"the":[26,43,48,61,67,87,105,116,142,185],"segments":[28],"representing":[29],"any":[30],"two":[31],"adjacent":[32],"nodes":[33],"are":[36],"vertically":[37],"visible":[38],"to":[39,129,211],"other.":[41],"present":[44],"paper":[45],"we":[46,196],"give":[47,197],"best":[49,117,186],"known":[50,119,187],"compact":[51],"G.":[55],"Given":[56],"canonical":[58,80],"ordering":[59],"triangulated":[62,88],"our":[64,156,174],"algorithm":[65,103,120],"draws":[66],"graph":[68],"incrementally":[69],"in":[70],"greedy":[72],"manner.":[73],"We":[74],"show":[75],"one":[77],"three":[79],"orderings":[81],"obtained":[82],"from":[83],"Schnyder's":[84],"realizer":[85],"for":[86,108,159,177,202],"yields":[90],"no":[96,149,162,180],"wider":[97,163,181],"than":[98,164,182],"$\\left\\lfloor{\\frac{22n-40}{15}}\\right\\rfloor$.":[99],"Our":[100,123],"easy-to-implement":[101],"O(n)-time":[102],"bypasses":[104],"complicated":[106],"subroutines":[107],"four-connected":[109],"components":[110],"and":[111,191,215],"four-block":[112],"trees":[113],"required":[114,143],"previously":[118],"Kant.":[122],"result":[124,188],"provides":[125],"negative":[127],"answer":[128],"Kant's":[130],"open":[131],"question":[132],"about":[133],"whether":[134],"$\\left\\lfloor{\\frac{3n-6}{2}}\\right\\rfloor$":[135],"worst-case":[138],"lower":[139],"bound":[140],"on":[141,208],"width.":[144],"Also,":[145],"if":[146,169],"has":[148],"degree-three":[150],"(respectively,":[151,166],"degree-five)":[152],"internal":[153],"node,":[154],"then":[155,173],"$\\left\\lfloor{\\frac{4n-9}{3}}\\right\\rfloor$":[165],"$\\left\\lfloor{\\frac{4n-7}{3}}\\right\\rfloor$).":[167],"Moreover,":[168],"four-connected,":[172],"n-1,":[183],"matching":[184],"Kant":[190],"He.":[192],"As":[193],"by-product,":[195],"much":[199],"simpler":[200],"proof":[201],"corollary":[204],"Wagner's":[206],"theorem":[207],"realizers":[209],"due":[210],"Bonichon,":[212],"Le":[213],"Sa\u00ebc,":[214],"Mosbah.":[216]},"counts_by_year":[{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2016-06-24T00:00:00"}