{"id":"https://openalex.org/W2064444401","doi":"https://doi.org/10.1137/080744694","title":"Line Transversals of Convex Polyhedra in $\\mathbb{R}^3$","display_name":"Line Transversals of Convex Polyhedra in $\\mathbb{R}^3$","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2064444401","doi":"https://doi.org/10.1137/080744694","mag":"2064444401"},"language":"en","primary_location":{"id":"doi:10.1137/080744694","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080744694","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/A5006699796","display_name":"Haim Kaplan","orcid":"https://orcid.org/0000-0001-9586-8002"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Haim Kaplan","raw_affiliation_strings":["haimk@post.tau.ac.il and rubinnat@post.tau.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"haimk@post.tau.ac.il and rubinnat@post.tau.ac.il#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014573012","display_name":"Natan Rubin","orcid":"https://orcid.org/0000-0002-7463-6728"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Natan Rubin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["michas@post.tau.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"michas@post.tau.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006699796"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3455,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.93373494,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"39","issue":"7","first_page":"3283","last_page":"3310"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.998199999332428,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.996999979019165,"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/combinatorics","display_name":"Combinatorics","score":0.8713663816452026},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.794952929019928},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7894337177276611},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6539688110351562},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6070850491523743},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5054130554199219},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.45060136914253235},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4163815379142761},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3863590955734253},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.17539334297180176},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07718512415885925}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8713663816452026},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.794952929019928},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7894337177276611},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6539688110351562},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6070850491523743},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5054130554199219},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45060136914253235},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4163815379142761},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3863590955734253},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.17539334297180176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07718512415885925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080744694","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080744694","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1509442273","https://openalex.org/W1564550597","https://openalex.org/W1973877592","https://openalex.org/W1977464163","https://openalex.org/W1993647398","https://openalex.org/W1995723550","https://openalex.org/W2009564521","https://openalex.org/W2011387411","https://openalex.org/W2020590137","https://openalex.org/W2028747718","https://openalex.org/W2031262594","https://openalex.org/W2040904149","https://openalex.org/W2043572918","https://openalex.org/W2055042442","https://openalex.org/W2058432138","https://openalex.org/W2064428342","https://openalex.org/W2066191916","https://openalex.org/W2068720912","https://openalex.org/W2083046806","https://openalex.org/W2089715871","https://openalex.org/W2094649462","https://openalex.org/W2100823012","https://openalex.org/W2101502605","https://openalex.org/W2113830395","https://openalex.org/W2114914255","https://openalex.org/W2117515078","https://openalex.org/W2125685982","https://openalex.org/W2128370376","https://openalex.org/W2130642806","https://openalex.org/W2132063258","https://openalex.org/W2156014405","https://openalex.org/W2162224965","https://openalex.org/W3138987285","https://openalex.org/W4213170981","https://openalex.org/W4232425010","https://openalex.org/W4254977685"],"related_works":["https://openalex.org/W2971340537","https://openalex.org/W2797788337","https://openalex.org/W2113001792","https://openalex.org/W2046210743","https://openalex.org/W1511346678","https://openalex.org/W2030136392","https://openalex.org/W2738111169","https://openalex.org/W1584292662","https://openalex.org/W1857475410","https://openalex.org/W4386395423"],"abstract_inverted_index":{"We":[0,227],"establish":[1,100],"a":[2,21,31,39,96,114,181,201,229],"bound":[3,104],"of":[4,13,17,20,24,33,46,65,90,105,110,131,139,154,168,176,193,197,200,204,214,222],"$O(n^2k^{1+\\varepsilon})$,":[5],"for":[6,128,145],"any":[7],"$\\varepsilon>0$,":[8],"on":[9,59,107,233],"the":[10,14,44,56,60,69,82,87,108,129,137,152,159,166,171,174,191,195,212,219],"combinatorial":[11,126],"complexity":[12,61,109,130],"set":[15,88,142],"$\\mathcal{T}$":[16,47,66],"line":[18,91,98,220],"transversals":[19,92,221],"collection":[22,202],"$\\mathcal{P}$":[23,155,177],"k":[25,205],"convex":[26,207],"polyhedra":[27,153,167,175],"in":[28,48,78,120,136,180,209,217],"$\\mathbb{R}^3$":[29],"with":[30],"total":[32],"n":[34],"facets,":[35],"and":[36,112,133,170],"we":[37,85],"present":[38],"randomized":[40,115],"algorithm":[41,116],"which":[42,74,93,117,218],"computes":[43,118],"boundary":[45],"comparable":[49,121,134],"expected":[50,122],"time.":[51,123],"Thus,":[52],"when":[53],"$k\\ll":[54],"n$,":[55],"new":[57,230],"bounds":[58,127],"(and":[62],"construction":[63],"cost)":[64],"improve":[67],"upon":[68],"previously":[70],"best":[71],"known":[72],"bounds,":[73],"are":[75,143,156,178],"nearly":[76],"cubic":[77],"n.":[79],"To":[80],"obtain":[81,228],"above":[83],"result,":[84],"study":[86],"$\\mathcal{T}_{\\ell_0}$":[89,119,132],"emanate":[94],"from":[95,165],"fixed":[97],"$\\ell_0$,":[99],"an":[101],"almost":[102],"tight":[103],"$O(nk^{1+\\varepsilon})$":[106],"$\\mathcal{T}_{\\ell_0}$,":[111],"provide":[113],"Slightly":[124],"improved":[125],"improvements":[135],"cost":[138],"constructing":[140],"this":[141,234],"established":[144],"two":[146],"special":[147],"cases,":[148],"both":[149],"assuming":[150],"that":[151],"pairwise":[157],"disjoint:":[158],"case":[160,172],"where":[161,173],"$\\ell_0$":[162],"is":[163,188],"disjoint":[164],"$\\mathcal{P}$,":[169],"unbounded":[179],"direction":[182],"parallel":[183],"to":[184,190],"$\\ell_0$.":[185],"Our":[186],"result":[187,232],"related":[189],"problem":[192],"bounding":[194],"number":[196,213],"geometric":[198],"permutations":[199],"$\\mathcal{C}$":[203,223],"pairwise-disjoint":[206],"sets":[208],"$\\mathbb{R}^3$,":[210],"namely,":[211],"distinct":[215],"orders":[216],"visit":[224],"its":[225],"members.":[226],"partial":[231],"problem.":[235]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
