{"id":"https://openalex.org/W3048972113","doi":"https://doi.org/10.1007/s00454-020-00232-w","title":"Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane","display_name":"Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane","publication_year":2020,"publication_date":"2020-08-11","ids":{"openalex":"https://openalex.org/W3048972113","doi":"https://doi.org/10.1007/s00454-020-00232-w","mag":"3048972113"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-020-00232-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00232-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00232-w.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00232-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017343893","display_name":"Mikkel Abrahamsen","orcid":"https://orcid.org/0000-0003-2734-4690"},"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":"Mikkel Abrahamsen","raw_affiliation_strings":["Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Universitetsparken 1, 2100 Copenhagen, Denmark","Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Universitetsparken\u00a01, 2100, Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Universitetsparken 1, 2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"Basic Algorithms Research Copenhagen (BARC), University of Copenhagen, Universitetsparken\u00a01, 2100, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001427452","display_name":"Panos Giannopoulos","orcid":"https://orcid.org/0000-0002-6261-1961"},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Panos Giannopoulos","raw_affiliation_strings":["giCenter, Department of Computer Science, City University of London, London EC1V 0HB, United Kingdom","giCenter, Department of Computer Science, City University of London, London, EC1V 0HB, United Kingdom"],"affiliations":[{"raw_affiliation_string":"giCenter, Department of Computer Science, City University of London, London EC1V 0HB, United Kingdom","institution_ids":["https://openalex.org/I180825142"]},{"raw_affiliation_string":"giCenter, Department of Computer Science, City University of London, London, EC1V 0HB, United Kingdom","institution_ids":["https://openalex.org/I180825142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112453554","display_name":"Maarten L\u00f6ffler","orcid":null},"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":false,"raw_author_name":"Maarten L\u00f6ffler","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083387191","display_name":"G\u00fcnter Rote","orcid":"https://orcid.org/0000-0002-0351-5945"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"G\u00fcnter Rote","raw_affiliation_strings":["Institut fr Informatik, Freie Universitt Berlin, Takustrae 9, 14195 Berlin, Germany 123","Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, 14195, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut fr Informatik, Freie Universitt Berlin, Takustrae 9, 14195 Berlin, Germany 123","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083387191"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.4483,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86736002,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"64","issue":"3","first_page":"575","last_page":"607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9891999959945679,"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/algorithm","display_name":"Algorithm","score":0.5914822220802307},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.45024868845939636},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41338905692100525},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4070979058742523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33976495265960693},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33701324462890625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2762018144130707}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5914822220802307},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.45024868845939636},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41338905692100525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4070979058742523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33976495265960693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33701324462890625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2762018144130707}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00454-020-00232-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00232-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00232-w.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:openaccess.city.ac.uk:24746","is_oa":false,"landing_page_url":"https://openaccess.city.ac.uk/view/creators_id/panos=2Egiannopoulos.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401940","display_name":"City Research Online (City University London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I180825142","host_organization_name":"City, University of London","host_organization_lineage":["https://openalex.org/I180825142"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:1902.04045","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.04045","pdf_url":"https://arxiv.org/pdf/1902.04045","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/a72cc365-a8db-4f60-b6fc-950295d99fac","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/a72cc365-a8db-4f60-b6fc-950295d99fac","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":"Abrahamsen , M , Giannopoulos , P , L\u00f6ffler , M & Rote , G 2020 , ' Geometric Multicut : Shortest Fences for Separating Groups of Objects in the Plane ' , Discrete & Computational Geometry , vol. 64 , pp. 575\u2013607 . https://doi.org/10.1007/s00454-020-00232-w","raw_type":"article"},{"id":"pmh:oai:refubium.fu-berlin.de:fub188/30703","is_oa":true,"landing_page_url":"https://refubium.fu-berlin.de/handle/fub188/30703","pdf_url":null,"source":{"id":"https://openalex.org/S4306402444","display_name":"Refubium (Universit\u00e4tsbibliothek der Freien Universit\u00e4t Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I75951250","host_organization_name":"Freie Universit\u00e4t Berlin","host_organization_lineage":["https://openalex.org/I75951250"],"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":"doc-type:article"},{"id":"doi:10.17169/refubium-30442","is_oa":true,"landing_page_url":"https://doi.org/10.17169/refubium-30442","pdf_url":null,"source":{"id":"https://openalex.org/S7407052913","display_name":"Universit\u00e4tsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.4230/lipics.icalp.2019.9","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2019.9","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"doi:10.1007/s00454-020-00232-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00232-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00232-w.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1084937899","display_name":null,"funder_award_id":"16582","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G1341482105","display_name":null,"funder_award_id":"614.001.504","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4422840520","display_name":null,"funder_award_id":"16582","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G6028897716","display_name":null,"funder_award_id":"DABAI","funder_id":"https://openalex.org/F4320313796","funder_display_name":"Innovationsfonden"},{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320313796","display_name":"Innovationsfonden","ror":"https://ror.org/00daj4111"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320328306","display_name":"Lorentz Center","ror":"https://ror.org/00d503m77"},{"id":"https://openalex.org/F4320334966","display_name":"Bhabha Atomic Research Centre","ror":"https://ror.org/05w6wfp17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3048972113.pdf","grobid_xml":"https://content.openalex.org/works/W3048972113.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W79315950","https://openalex.org/W1887122289","https://openalex.org/W1967191875","https://openalex.org/W2015696135","https://openalex.org/W2060121592","https://openalex.org/W2060380213","https://openalex.org/W2063514882","https://openalex.org/W2067636581","https://openalex.org/W2086709935","https://openalex.org/W2087675574","https://openalex.org/W2116909526","https://openalex.org/W2119378898","https://openalex.org/W2152986618","https://openalex.org/W2167236203","https://openalex.org/W2172544626","https://openalex.org/W2278003675","https://openalex.org/W2570865945","https://openalex.org/W2741786970","https://openalex.org/W2795402084","https://openalex.org/W3009415557","https://openalex.org/W3037475288","https://openalex.org/W3121576764","https://openalex.org/W3172501025","https://openalex.org/W4233880474","https://openalex.org/W4293415950"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W4256429076","https://openalex.org/W1971174658","https://openalex.org/W2007980826","https://openalex.org/W2099195351","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819"],"abstract_inverted_index":{"Abstract":[0],"We":[1,70,94,126],"study":[2],"the":[3,16,62,65,68,73,88,110,113,130,135],"following":[4],"separation":[5],"problem:":[6],"Given":[7],"a":[8,23,29,53,84,143],"collection":[9],"of":[10,31,33,41,43,116,118,137,156],"pairwise":[11],"disjoint":[12],"coloured":[13],"objects":[14,42,47],"in":[15,61,67,124],"plane":[17],"with":[18,121],"k":[19,77],"different":[20,44],"colours,":[21],"compute":[22],"shortest":[24],"\u201cfence\u201d":[25],"F":[26,51],",":[27,80],"i.e.,":[28],"union":[30],"curves":[32],"minimum":[34],"total":[35],"length,":[36],"that":[37,57,104,129],"separates":[38],"every":[39],"pair":[40],"colours.":[45,139,157],"Two":[46],"are":[48],"separated":[49],"if":[50],"contains":[52],"simple":[54],"closed":[55],"curve":[56],"has":[58],"one":[59],"object":[60],"interior":[63],"and":[64,153],"other":[66],"exterior.":[69],"refer":[71],"to":[72,87],"problem":[74,91,131],"as":[75,81],"geometric":[76,85],"-":[78],"cut":[79],"it":[82],"is":[83,132],"analog":[86],"well-studied":[89],"multicut":[90],"on":[92],"graphs.":[93],"first":[95],"give":[96,142],"an":[97,106],"$$O(n^4\\log":[98],"^3\\!n)$$":[99],"<mml:math":[100,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:msup><mml:mo>log</mml:mo><mml:mn>3</mml:mn></mml:msup><mml:mspace/><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>":[101],"-time":[102],"algorithm":[103,150],"computes":[105],"optimal":[107],"fence":[108],"for":[109,134,151],"case":[111,136],"where":[112],"input":[114],"consists":[115],"polygons":[117,152],"two":[119],"colours":[120],"n":[122],"corners":[123],"total.":[125],"then":[127],"show":[128],"NP-hard":[133],"three":[138],"Finally,":[140],"we":[141],"randomised":[144],"$$4/3\\cdot":[145],"1.2965$$":[146],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mn>4</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn><mml:mo>\u00b7</mml:mo><mml:mn>1.2965</mml:mn></mml:mrow></mml:math>":[148],"-approximation":[149],"any":[154],"number":[155]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2020-08-18T00:00:00"}
