{"id":"https://openalex.org/W2014312515","doi":"https://doi.org/10.1145/1377676.1377691","title":"On levels in arrangements of curves, iii","display_name":"On levels in arrangements of curves, iii","publication_year":2008,"publication_date":"2008-06-09","ids":{"openalex":"https://openalex.org/W2014312515","doi":"https://doi.org/10.1145/1377676.1377691","mag":"2014312515"},"language":"en","primary_location":{"id":"doi:10.1145/1377676.1377691","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377676.1377691","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fourth annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032955418","display_name":"Timothy M. Chan","orcid":"https://orcid.org/0000-0002-8093-0675"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Timothy M. Chan","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032955418"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":2.9771,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.91146754,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"85","last_page":"93"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"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":1.0,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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/bounding-overwatch","display_name":"Bounding overwatch","score":0.8228558301925659},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5348932147026062},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4524763822555542},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44302263855934143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3824306130409241},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33776670694351196},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27768850326538086},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09410196542739868}],"concepts":[{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.8228558301925659},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5348932147026062},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4524763822555542},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44302263855934143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824306130409241},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33776670694351196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27768850326538086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09410196542739868}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1377676.1377691","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377676.1377691","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fourth annual symposium on Computational geometry","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W117619795","https://openalex.org/W1517439050","https://openalex.org/W1974343573","https://openalex.org/W1986004959","https://openalex.org/W2016890960","https://openalex.org/W2019227847","https://openalex.org/W2021751455","https://openalex.org/W2035884884","https://openalex.org/W2036637777","https://openalex.org/W2039157981","https://openalex.org/W2058432138","https://openalex.org/W2094683955","https://openalex.org/W2149757010","https://openalex.org/W2155476808","https://openalex.org/W2157282884","https://openalex.org/W2163913133","https://openalex.org/W2164723212","https://openalex.org/W2167163837","https://openalex.org/W3147681132","https://openalex.org/W4254977685"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"We":[0,19],"revisit":[1],"the":[2,6,10,27,30],"problem":[3],"of":[4,9,16,23],"bounding":[5],"combinatorial":[7],"complexity":[8],"k-level":[11],"in":[12],"a":[13,21],"two-dimensional":[14],"arrangement":[15],"n":[17],"curves.":[18],"give":[20],"number":[22],"small":[24],"improvements":[25],"over":[26],"results":[28],"from":[29],"author's":[31],"previous":[32],"paper":[33],"(FOCS'03).":[34],"For":[35],"example:":[36]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
