{"id":"https://openalex.org/W2087654340","doi":"https://doi.org/10.1137/0214046","title":"An $O(E\\log E + I)$ Expected Time Algorithm for the Planar Segment Intersection Problem","display_name":"An $O(E\\log E + I)$ Expected Time Algorithm for the Planar Segment Intersection Problem","publication_year":1985,"publication_date":"1985-08-01","ids":{"openalex":"https://openalex.org/W2087654340","doi":"https://doi.org/10.1137/0214046","mag":"2087654340"},"language":"en","primary_location":{"id":"doi:10.1137/0214046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214046","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068657716","display_name":"Eugene W. Myers","orcid":"https://orcid.org/0000-0002-6580-7839"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eugene W. Myers","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068657716"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6031,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.83235294,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"625","last_page":"637"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/intersection","display_name":"Intersection (aeronautics)","score":0.7337032556533813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6846786737442017},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6141221523284912},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5858098268508911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5777215361595154},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4945923984050751},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.47380512952804565},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.46489089727401733},{"id":"https://openalex.org/keywords/analysis-of-algorithms","display_name":"Analysis of algorithms","score":0.46435999870300293},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.45602530241012573},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4438551366329193},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4372062683105469},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.41521143913269043},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.4143315255641937},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35263577103614807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3043757677078247},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1217339038848877}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7337032556533813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6846786737442017},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6141221523284912},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5858098268508911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5777215361595154},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4945923984050751},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.47380512952804565},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.46489089727401733},{"id":"https://openalex.org/C64731005","wikidata":"https://www.wikidata.org/wiki/Q333464","display_name":"Analysis of algorithms","level":2,"score":0.46435999870300293},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.45602530241012573},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4438551366329193},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4372062683105469},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.41521143913269043},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.4143315255641937},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35263577103614807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3043757677078247},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1217339038848877},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0214046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214046","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1874694348","https://openalex.org/W1991651582","https://openalex.org/W1999447420","https://openalex.org/W2006749054","https://openalex.org/W2011318166","https://openalex.org/W2017493520","https://openalex.org/W2030641205","https://openalex.org/W2059575356","https://openalex.org/W2068376033","https://openalex.org/W2101347629","https://openalex.org/W2151335991","https://openalex.org/W2304328429"],"related_works":["https://openalex.org/W2007715402","https://openalex.org/W2011903683","https://openalex.org/W2042426695","https://openalex.org/W2737119934","https://openalex.org/W2029469528","https://openalex.org/W2004524662","https://openalex.org/W2009283111","https://openalex.org/W2150861432","https://openalex.org/W1575958304","https://openalex.org/W1974844978"],"abstract_inverted_index":{"It":[0],"is":[1,46],"an":[2,13],"open":[3],"question":[4],"in":[5,31,95],"computational":[6],"geometry":[7],"as":[8,69],"to":[9,19,97],"whether":[10],"there":[11],"exists":[12],"$O(E\\log":[14,52,83],"E":[15,28,53,84],"+":[16,54,85],"I)$":[17,55],"algorithm":[18,50,64,71,89],"determine":[20],"the":[21,32,60,63,66,70,105,108],"I":[22],"intersections":[23],"of":[24,27,72,107],"a":[25,37,43],"collection":[26],"line":[29],"segments":[30],"plane.":[33],"An":[34],"approach":[35],"utilizing":[36],"work":[38],"list":[39],"bubble":[40],"sort":[41],"and":[42,74,94],"distribution-based":[44],"search":[45],"presented.":[47],"The":[48,88],"resulting":[49],"has":[51,65],"expected":[56],"time":[57],"complexity.":[58],"In":[59],"worst":[61],"case":[62],"same":[67],"complexity":[68],"Bentley":[73],"Ottmann":[75],"[IEEE":[76],"Trans.":[77],"Comput.,":[78],"28":[79],"(1979),":[80],"pp.":[81],"643\u2013647]:":[82],"I\\log":[86],"E)$.":[87],"requires":[90],"only":[91],"$O(E)$":[92],"space":[93],"contrast":[96],"prior":[98],"work,":[99],"no":[100],"restrictions":[101],"are":[102],"placed":[103],"upon":[104],"nature":[106],"intersections.":[109]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}