{"id":"https://openalex.org/W2767474623","doi":"https://doi.org/10.3390/ijgi6110342","title":"Beyond Maximum Independent Set: An Extended Integer Programming Formulation for Point Labeling","display_name":"Beyond Maximum Independent Set: An Extended Integer Programming Formulation for Point Labeling","publication_year":2017,"publication_date":"2017-11-06","ids":{"openalex":"https://openalex.org/W2767474623","doi":"https://doi.org/10.3390/ijgi6110342","mag":"2767474623"},"language":"en","primary_location":{"id":"doi:10.3390/ijgi6110342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi6110342","pdf_url":"https://www.mdpi.com/2220-9964/6/11/342/pdf?version=1509962368","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2220-9964/6/11/342/pdf?version=1509962368","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049298894","display_name":"Jan\u2010Henrik Haunert","orcid":"https://orcid.org/0000-0001-8005-943X"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jan-Henrik Haunert","raw_affiliation_strings":["Institute of Geodesy and Geoinformation, University of Bonn, 53115 Bonn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Geodesy and Geoinformation, University of Bonn, 53115 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014138072","display_name":"Alexander Wolff","orcid":"https://orcid.org/0000-0001-5872-718X"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexander Wolff","raw_affiliation_strings":["Institut f\u00fcr Informatik, Universit\u00e4t W\u00fcrzburg, 97074 W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Universit\u00e4t W\u00fcrzburg, 97074 W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014138072","https://openalex.org/A5049298894"],"corresponding_institution_ids":["https://openalex.org/I135140700","https://openalex.org/I25974101"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":833,"currency":"EUR","value_usd":898},"fwci":1.1201,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.79871637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":"11","first_page":"342","last_page":"342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980999827384949,"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/T10757","display_name":"Geographic Information Systems Studies","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/3305","display_name":"Geography, Planning and Development"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.748877227306366},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.71788090467453},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.6579182147979736},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.654749870300293},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.6427246332168579},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6113702058792114},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5966528058052063},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5364475846290588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5249152779579163},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5231060981750488},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45973291993141174},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4168263077735901},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4157716929912567},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39362356066703796},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36860033869743347},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.32287532091140747}],"concepts":[{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.748877227306366},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.71788090467453},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.6579182147979736},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.654749870300293},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.6427246332168579},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6113702058792114},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5966528058052063},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5364475846290588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5249152779579163},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5231060981750488},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45973291993141174},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4168263077735901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4157716929912567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39362356066703796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36860033869743347},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.32287532091140747},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/ijgi6110342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi6110342","pdf_url":"https://www.mdpi.com/2220-9964/6/11/342/pdf?version=1509962368","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:110d659d762e47ef9c778c69de88bc1b","is_oa":false,"landing_page_url":"https://doaj.org/article/110d659d762e47ef9c778c69de88bc1b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISPRS International Journal of Geo-Information, Vol 6, Iss 11, p 342 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2220-9964/6/11/342/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/ijgi6110342","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"ISPRS International Journal of Geo-Information; Volume 6; Issue 11; Pages: 342","raw_type":"Text"},{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:15896","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/15896","pdf_url":null,"source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"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":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/ijgi6110342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi6110342","pdf_url":"https://www.mdpi.com/2220-9964/6/11/342/pdf?version=1509962368","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W83093243","https://openalex.org/W1485435901","https://openalex.org/W1487629301","https://openalex.org/W1544357472","https://openalex.org/W1553915811","https://openalex.org/W1766493433","https://openalex.org/W1861355917","https://openalex.org/W1968143987","https://openalex.org/W1969744418","https://openalex.org/W1980797658","https://openalex.org/W1981556893","https://openalex.org/W1985369116","https://openalex.org/W1992210522","https://openalex.org/W1996136679","https://openalex.org/W2000080109","https://openalex.org/W2000386588","https://openalex.org/W2003147630","https://openalex.org/W2020353019","https://openalex.org/W2032299552","https://openalex.org/W2067819296","https://openalex.org/W2068162927","https://openalex.org/W2069559103","https://openalex.org/W2076213041","https://openalex.org/W2104936608","https://openalex.org/W2110282707","https://openalex.org/W2110348081","https://openalex.org/W2138350120","https://openalex.org/W2150801382","https://openalex.org/W2155332641","https://openalex.org/W2161540720","https://openalex.org/W2169753586","https://openalex.org/W2419059996","https://openalex.org/W2482846108","https://openalex.org/W2505968561","https://openalex.org/W2619738444","https://openalex.org/W2983296203","https://openalex.org/W4241362031","https://openalex.org/W4245143546","https://openalex.org/W4251391716","https://openalex.org/W4285719527","https://openalex.org/W6607633409","https://openalex.org/W6637897358","https://openalex.org/W6655522375","https://openalex.org/W6676638889","https://openalex.org/W6683841410"],"related_works":["https://openalex.org/W4252122881","https://openalex.org/W134055995","https://openalex.org/W2009796757","https://openalex.org/W1925942709","https://openalex.org/W4302819359","https://openalex.org/W1963627056","https://openalex.org/W2047683846","https://openalex.org/W2044902158","https://openalex.org/W1973873435","https://openalex.org/W4232431455"],"abstract_inverted_index":{"Map":[0],"labeling":[1,47],"is":[2,36,154],"a":[3,17,22,28,33,46,116,170,208,215],"classical":[4],"problem":[5,35,153],"of":[6,19,30,42,69,89,101,106,139,172,205,210],"cartography":[7],"that":[8,51,96],"has":[9],"frequently":[10],"been":[11],"approached":[12],"by":[13],"combinatorial":[14],"optimization.":[15],"Given":[16],"set":[18,29,41,204],"features":[20],"in":[21,115,188],"map":[23,129],"and":[24,58,78,126,200,217],"for":[25,63,159,164,195,214,224],"each":[26,64],"feature":[27],"label":[31,62],"candidates,":[32],"common":[34],"to":[37,122,143,184],"select":[38],"an":[39,140,160,176,201],"independent":[40],"labels":[43,55,74,107,110,120],"(that":[44],"is,":[45],"without":[48,149],"label\u2013label":[49],"intersections)":[50],"contains":[52],"as":[53,56,175],"many":[54],"possible":[57],"at":[59],"most":[60],"one":[61,79],"feature.":[65],"To":[66],"obtain":[67],"solutions":[68,187,223],"high":[70],"cartographic":[71],"quality,":[72],"the":[73,82,87,90,99,102,104,119,128,152,165],"can":[75,80,131],"be":[76,123,132],"weighted":[77],"maximize":[81],"total":[83],"weight":[84,100],"(rather":[85],"than":[86],"number)":[88],"selected":[91],"labels.":[92],"We":[93,136],"argue,":[94],"however,":[95],"when":[97],"maximizing":[98],"labeling,":[103,118],"influences":[105],"on":[108],"other":[109],"are":[111],"insufficiently":[112],"addressed.":[113],"Furthermore,":[114],"maximum-weight":[117],"tend":[121],"densely":[124],"packed":[125],"thus":[127],"background":[130],"occluded":[133],"too":[134],"much.":[135],"propose":[137],"extensions":[138,151],"existing":[141,202],"model":[142,174],"overcome":[144],"these":[145],"limitations.":[146],"Since":[147],"even":[148],"our":[150,173,211,225],"NP-hard,":[155],"we":[156,168,192],"cannot":[157],"hope":[158],"efficient":[161,218],"exact":[162],"algorithm":[163],"problem.":[166],"Therefore,":[167],"present":[169],"formalization":[171],"integer":[177],"linear":[178],"program":[179],"(ILP).":[180],"This":[181],"allows":[182,213],"us":[183],"compute":[185],"optimal":[186],"reasonable":[189],"time,":[190],"which":[191,220],"demonstrate":[193],"both":[194],"randomly":[196],"generated":[197],"point":[198],"sets":[199],"data":[203],"cities.":[206],"Moreover,":[207],"relaxation":[209],"ILP":[212],"simple":[216],"heuristic,":[219],"yielded":[221],"near-optimal":[222],"instances.":[226]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2017-11-17T00:00:00"}