{"id":"https://openalex.org/W1525153939","doi":"https://doi.org/10.1137/s0097539799358835","title":"Covering Rectilinear Polygons with Axis-Parallel Rectangles","display_name":"Covering Rectilinear Polygons with Axis-Parallel Rectangles","publication_year":1999,"publication_date":"1999-05-01","ids":{"openalex":"https://openalex.org/W1525153939","doi":"https://doi.org/10.1137/s0097539799358835","mag":"1525153939"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539799358835","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539799358835","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/301250.301369","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101673409","display_name":"Vijay Kumar","orcid":"https://orcid.org/0000-0002-2996-7181"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["DE","IN"],"is_corresponding":true,"raw_author_name":"V. S. Anil Kumar","raw_affiliation_strings":["Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":null,"display_name":"H. Ramesh","orcid":null},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["DE","IN"],"is_corresponding":false,"raw_author_name":"H. Ramesh","raw_affiliation_strings":["Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101673409"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.6764,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.70216777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"6","first_page":"1509","last_page":"1541"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9887999892234802,"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":0.9887999892234802,"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/T12504","display_name":"Mathematics and Applications","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.9282000064849854,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rectilinear-polygon","display_name":"Rectilinear polygon","score":0.5464157462120056},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.5240590572357178},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42526113986968994},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4212892949581146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41139835119247437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3863860070705414},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3528894782066345},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.27541929483413696},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.1259492039680481}],"concepts":[{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.5464157462120056},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.5240590572357178},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42526113986968994},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4212892949581146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41139835119247437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3863860070705414},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3528894782066345},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.27541929483413696},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.1259492039680481},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0097539799358835","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539799358835","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},{"id":"doi:10.1145/301250.301369","is_oa":true,"landing_page_url":"https://doi.org/10.1145/301250.301369","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/301250.301369","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-first annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:edoc.mpg.de:518050","is_oa":false,"landing_page_url":"http://edoc.mpg.de/518050","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC-99), ACM, 445-454 (1999)","raw_type":"Conference-Paper"},{"id":"pmh:oai:pure.mpg.de:item_1331110","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-35B4-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC-99)","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"mag:1525153939","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1331110","pdf_url":null,"source":{"id":"https://openalex.org/S4306533943","display_name":"Untitled Event","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Untitled Event","raw_type":null}],"best_oa_location":{"id":"doi:10.1145/301250.301369","is_oa":true,"landing_page_url":"https://doi.org/10.1145/301250.301369","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/301250.301369","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-first annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/2","score":0.41999998688697815,"display_name":"Zero hunger"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1525153939.pdf","grobid_xml":"https://content.openalex.org/works/W1525153939.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1966613935","https://openalex.org/W1978186063","https://openalex.org/W2003159902","https://openalex.org/W2022671649","https://openalex.org/W2040924621","https://openalex.org/W2069462265","https://openalex.org/W2069664592","https://openalex.org/W2073450824","https://openalex.org/W2079473728","https://openalex.org/W2088027604","https://openalex.org/W2097577161","https://openalex.org/W2122642270","https://openalex.org/W2163322487"],"related_works":["https://openalex.org/W577875889","https://openalex.org/W2022671649","https://openalex.org/W2028175753","https://openalex.org/W2972529991","https://openalex.org/W1972470900","https://openalex.org/W2005465277","https://openalex.org/W3204453854","https://openalex.org/W2094795489","https://openalex.org/W68166563","https://openalex.org/W2359829522","https://openalex.org/W1535195895","https://openalex.org/W583845173","https://openalex.org/W2049280304","https://openalex.org/W2108676160","https://openalex.org/W2138346897","https://openalex.org/W2220505770","https://openalex.org/W3089296195","https://openalex.org/W3044037493","https://openalex.org/W2382748940","https://openalex.org/W2947706101"],"abstract_inverted_index":{"We":[0],"give":[1],"an":[2,30],"$O(\\sqrt{\\log":[3],"n})$":[4],"factor":[5],"approximation":[6,24,33],"algorithm":[7,25],"for":[8,26],"covering":[9],"a":[10],"rectilinear":[11],"polygon":[12],"with":[13,29],"holes":[14],"using":[15],"axis-parallel":[16],"rectangles.":[17],"This":[18],"is":[19],"the":[20],"first":[21],"polynomial":[22],"time":[23],"this":[27],"problem":[28],"$o(\\log":[31],"n)$":[32],"factor.":[34]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}