{"id":"https://openalex.org/W3191260606","doi":"https://doi.org/10.1007/s00454-023-00540-x","title":"Topological Art in Simple Galleries","display_name":"Topological Art in Simple Galleries","publication_year":2023,"publication_date":"2023-08-27","ids":{"openalex":"https://openalex.org/W3191260606","doi":"https://doi.org/10.1007/s00454-023-00540-x","mag":"3191260606"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-023-00540-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00540-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00540-x.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00540-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053720453","display_name":"Daniel Bertschinger","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Daniel Bertschinger","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076367765","display_name":"Nicolas El Maalouly","orcid":"https://orcid.org/0000-0002-1037-0203"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Nicolas El Maalouly","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-1037-0203","affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077251333","display_name":"Tillmann Miltzow","orcid":"https://orcid.org/0000-0003-4563-2864"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Tillmann Miltzow","raw_affiliation_strings":["Deparment of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-4563-2864","affiliations":[{"raw_affiliation_string":"Deparment of Information and Computing Sciences, Utrecht University, Utrecht, Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000735637","display_name":"Patrick Schnider","orcid":"https://orcid.org/0000-0002-2172-9285"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Patrick Schnider","raw_affiliation_strings":["Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark"],"raw_orcid":"https://orcid.org/0000-0002-2172-9285","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011682995","display_name":"Simon Weber","orcid":"https://orcid.org/0000-0003-1901-3621"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Simon Weber","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-1901-3621","affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5077251333"],"corresponding_institution_ids":["https://openalex.org/I193662353"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.4482,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85988287,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"71","issue":"3","first_page":"1092","last_page":"1130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9847999811172485,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9545000195503235,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/simple","display_name":"Simple (philosophy)","score":0.8105716109275818},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5114259123802185},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3876708745956421},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3465091288089752},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33167654275894165},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2020154893398285},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.10788896679878235},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.07317611575126648}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8105716109275818},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5114259123802185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3876708745956421},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3465091288089752},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33167654275894165},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2020154893398285},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.10788896679878235},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.07317611575126648}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00454-023-00540-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00540-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00540-x.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:research-collection.ethz.ch:20.500.11850/652606","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/652606","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry, 71 (3)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dspace.library.uu.nl:1874/473233","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/473233","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/33718e45-fa79-4491-b230-a7ea3f84bb43","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/33718e45-fa79-4491-b230-a7ea3f84bb43","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bertschinger , D , El Maalouly , N , Miltzow , T , Schnider , P & Weber , S 2024 , ' Topological Art in Simple Galleries ' , Discrete and Computational Geometry , vol. 71 , pp. 1092\u20131130 . https://doi.org/10.1007/s00454-023-00540-x","raw_type":"article"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/415214","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/415214","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/other"},{"id":"doi:10.48550/arxiv.2108.04007","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2108.04007","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":"article-journal"},{"id":"doi:10.3929/ethz-b-000652606","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000652606","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00540-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00540-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00540-x.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.46000000834465027,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G220638465","display_name":null,"funder_award_id":"016.Veni.192.250","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6086961061","display_name":null,"funder_award_id":"ERC StG 716424","funder_id":"https://openalex.org/F4320333065","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G7010378412","display_name":null,"funder_award_id":"016.Veni","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320333065","display_name":"Seventh Framework Programme","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3191260606.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W67007978","https://openalex.org/W94985437","https://openalex.org/W176071698","https://openalex.org/W1980508374","https://openalex.org/W1981172165","https://openalex.org/W1987747840","https://openalex.org/W2006753964","https://openalex.org/W2033775003","https://openalex.org/W2038280788","https://openalex.org/W2041495686","https://openalex.org/W2060049097","https://openalex.org/W2063442090","https://openalex.org/W2087422927","https://openalex.org/W2094658339","https://openalex.org/W2102167981","https://openalex.org/W2110033738","https://openalex.org/W2115708125","https://openalex.org/W2143731699","https://openalex.org/W2284193075","https://openalex.org/W2510258722","https://openalex.org/W2546555264","https://openalex.org/W2560970889","https://openalex.org/W2566164082","https://openalex.org/W2573654584","https://openalex.org/W2612212426","https://openalex.org/W2899198588","https://openalex.org/W2937244017","https://openalex.org/W2962894880","https://openalex.org/W2963664653","https://openalex.org/W3035901889","https://openalex.org/W3037840582","https://openalex.org/W3040586665","https://openalex.org/W3120633265","https://openalex.org/W3128545493","https://openalex.org/W3130723092","https://openalex.org/W3156527047","https://openalex.org/W3166720684","https://openalex.org/W4235282062","https://openalex.org/W4242616223","https://openalex.org/W4254205555","https://openalex.org/W4255045236"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"P":[2,27,70,77,92,116,121],"be":[3],"a":[4,15,94,99,114],"simple":[5],"polygon,":[6],"then":[7],"the":[8,50,79,142],"art":[9,143],"gallery":[10,144],"problem":[11,145],"is":[12,67,113,123,152],"looking":[13],"for":[14,107,130],"minimum":[16,83],"set":[17,110],"of":[18,81,141],"points":[19,32],"(guards)":[20],"that":[21,105,118,147],"can":[22,45],"see":[23,46],"every":[24,108],"point":[25],"in":[26,69],".":[28,71,128,156],"We":[29,72,102],"say":[30],"two":[31],"$$a,b\\in":[33],"P$$":[34],"<mml:math":[35,56],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[36,57],"<mml:mrow>":[37,58],"<mml:mi>a</mml:mi>":[38,61],"<mml:mo>,</mml:mo>":[39,62],"<mml:mi>b</mml:mi>":[40,63],"<mml:mo>\u2208</mml:mo>":[41],"<mml:mi>P</mml:mi>":[42],"</mml:mrow>":[43,65],"</mml:math>":[44,66],"each":[47],"other":[48],"if":[49],"line":[51],"segment":[52],"$${\\text":[53],"{seg}}":[54],"(a,b)$$":[55],"<mml:mtext>seg</mml:mtext>":[59],"<mml:mo>(</mml:mo>":[60],"<mml:mo>)</mml:mo>":[64],"contained":[68],"denote":[73],"by":[74],"V":[75,90,119,148],"(":[76,91,120,149],")":[78,93,122,151],"family":[80],"all":[82],"guard":[84],"placements.":[85],"The":[86],"Hausdorff":[87],"distance":[88],"makes":[89],"metric":[95],"space":[96],"and":[97],"thus":[98],"topological":[100,133],"space.":[101],"show":[103],"homotopy-universality,":[104],"is,":[106],"semi-algebraic":[109],"S":[111,127],"there":[112],"polygon":[115],"such":[117,146],"homotopy":[124],"equivalent":[125],"to":[126,154],"Furthermore,":[129],"various":[131],"concrete":[132],"spaces":[134],"T":[135,155],",":[136],"we":[137],"describe":[138],"instances":[139],"I":[140,150],"homeomorphic":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}