{"id":"https://openalex.org/W2569307415","doi":"https://doi.org/10.1137/140955975","title":"Making Octants Colorful and Related Covering Decomposition Problems","display_name":"Making Octants Colorful and Related Covering Decomposition Problems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2569307415","doi":"https://doi.org/10.1137/140955975","mag":"2569307415"},"language":"en","primary_location":{"id":"doi:10.1137/140955975","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140955975","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ruj.uj.edu.pl/xmlui/handle/item/3925","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011369568","display_name":"Jean Cardinal","orcid":"https://orcid.org/0000-0002-2312-0967"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jean Cardinal","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057566451","display_name":"Kolja Knauer","orcid":"https://orcid.org/0000-0002-8151-2184"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kolja Knauer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107964690","display_name":"Piotr Micek","orcid":"https://orcid.org/0000-0001-9796-5375"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piotr Micek","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063296115","display_name":"Torsten Ueckerdt","orcid":"https://orcid.org/0000-0002-0645-9715"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Torsten Ueckerdt","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011369568"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1306,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92033786,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"4","first_page":"1948","last_page":"1959"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9538999795913696,"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":0.9538999795913696,"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":0.016300000250339508,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.005499999970197678,"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/homothetic-transformation","display_name":"Homothetic transformation","score":0.873473048210144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7873504161834717},{"id":"https://openalex.org/keywords/octant","display_name":"Octant (instrument)","score":0.7036594152450562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6960158348083496},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6299864649772644},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.606056809425354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47287601232528687},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4723314642906189},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4523537755012512},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44135695695877075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13192322850227356},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08090665936470032}],"concepts":[{"id":"https://openalex.org/C91709909","wikidata":"https://www.wikidata.org/wiki/Q583960","display_name":"Homothetic transformation","level":2,"score":0.873473048210144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7873504161834717},{"id":"https://openalex.org/C177994039","wikidata":"https://www.wikidata.org/wiki/Q427293","display_name":"Octant (instrument)","level":2,"score":0.7036594152450562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6960158348083496},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6299864649772644},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.606056809425354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47287601232528687},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4723314642906189},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4523537755012512},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44135695695877075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13192322850227356},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08090665936470032},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140955975","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140955975","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:ruj.uj.edu.pl:item/3925","is_oa":true,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/3925","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/192342","is_oa":false,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/192342","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on discrete mathematics, 28 (4","raw_type":"info:ulb-repo/semantics/openurl/article"}],"best_oa_location":{"id":"pmh:oai:ruj.uj.edu.pl:item/3925","is_oa":true,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/3925","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1745488587","https://openalex.org/W1843684924","https://openalex.org/W1982498410","https://openalex.org/W1984121377","https://openalex.org/W1986134212","https://openalex.org/W1999396007","https://openalex.org/W2001456750","https://openalex.org/W2004070233","https://openalex.org/W2013760641","https://openalex.org/W2016829899","https://openalex.org/W2025955201","https://openalex.org/W2038503671","https://openalex.org/W2043718124","https://openalex.org/W2052846058","https://openalex.org/W2053369727","https://openalex.org/W2064723783","https://openalex.org/W2077689859","https://openalex.org/W2143341942","https://openalex.org/W2155755180","https://openalex.org/W2220719914","https://openalex.org/W2514202683"],"related_works":["https://openalex.org/W2791665318","https://openalex.org/W4300615779","https://openalex.org/W2610034574","https://openalex.org/W3143729892","https://openalex.org/W2406295471","https://openalex.org/W2902492219","https://openalex.org/W1994989603","https://openalex.org/W2371284713","https://openalex.org/W4301012671","https://openalex.org/W2569307415"],"abstract_inverted_index":{"We":[0,88,100],"give":[1],"new":[2,119],"positive":[3,24],"results":[4],"on":[5,97],"the":[6,45,75,80,153],"long-standing":[7],"open":[8],"problem":[9],"of":[10,30,44,57,82,110,118,140,152],"geometric":[11],"covering":[12,113],"decomposition":[13,92,109],"for":[14,22,79,149],"homothetic":[15,86],"polygons.":[16],"In":[17],"particular,":[18],"we":[19],"prove":[20,101],"that":[21,41,102,136],"any":[23,146],"integer":[25],"$k$,":[26],"every":[27,42],"finite":[28],"set":[29],"points":[31,52],"in":[32,68,122,126],"$\\mathbb{R}^3$":[33],"can":[34,105,131],"be":[35,132],"colored":[36],"with":[37],"$k$":[38],"colors":[39],"so":[40],"translate":[43],"negative":[46],"octant":[47,154],"containing":[48],"at":[49,54],"least":[50,55],"$k^6$":[51],"contains":[53],"one":[56],"each":[58],"color.":[59],"The":[60],"best":[61],"previously":[62],"known":[63],"bound":[64,78,147],"was":[65],"doubly":[66],"exponential":[67],"$k$.":[69],"This":[70,134],"yields,":[71],"among":[72],"other":[73],"corollaries,":[74],"first":[76],"polynomial":[77],"decomposability":[81],"multiple":[83,112],"coverings":[84],"by":[85,114],"triangles.":[87],"also":[89],"investigate":[90],"related":[91],"problems":[93],"involving":[94],"intervals":[95,115],"appearing":[96],"a":[98,108,111,123,137],"line.":[99],"no":[103],"algorithm":[104],"dynamically":[106],"maintain":[107],"under":[116],"insertion":[117],"intervals,":[120],"even":[121,148],"semionline":[124],"model,":[125],"which":[127],"some":[128],"coloring":[129],"decisions":[130],"delayed.":[133],"implies":[135],"wide":[138],"range":[139],"sweeping":[141],"plane":[142],"algorithms":[143],"cannot":[144],"guarantee":[145],"special":[150],"cases":[151],"problem.":[155]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}