{"id":"https://openalex.org/W1780187217","doi":"https://doi.org/10.1137/070707130","title":"Spanners of Complete <i>k</i>-Partite Geometric Graphs","display_name":"Spanners of Complete <i>k</i>-Partite Geometric Graphs","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1780187217","doi":"https://doi.org/10.1137/070707130","mag":"1780187217"},"language":"en","primary_location":{"id":"doi:10.1137/070707130","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070707130","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/A5013674788","display_name":"Prosenjit Bose","orcid":"https://orcid.org/0000-0002-8906-0573"},"institutions":[{"id":"https://openalex.org/I188497080","display_name":"Carleton College","ror":"https://ror.org/03jep7677","country_code":"US","type":"education","lineage":["https://openalex.org/I188497080"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Prosenjit Bose","raw_affiliation_strings":["jit@cg.scs.carleton.ca and carmip@gmail.com and couturem@gmail.com and anil@scs.carleton.ca and morin@scs.carleton.ca and michiel.smid@gmail.com#TAB#"],"affiliations":[{"raw_affiliation_string":"jit@cg.scs.carleton.ca and carmip@gmail.com and couturem@gmail.com and anil@scs.carleton.ca and morin@scs.carleton.ca and michiel.smid@gmail.com#TAB#","institution_ids":["https://openalex.org/I188497080"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026094478","display_name":"Paz Carmi","orcid":"https://orcid.org/0000-0003-0154-5013"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Paz Carmi","raw_affiliation_strings":["#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087583066","display_name":"Mathieu Couture","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mathieu Couture","raw_affiliation_strings":["#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103136561","display_name":"Anil Maheshwari","orcid":"https://orcid.org/0000-0002-1274-4598"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Anil Maheshwari","raw_affiliation_strings":["#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045902784","display_name":"Pat Morin","orcid":"https://orcid.org/0000-0003-0471-4118"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pat Morin","raw_affiliation_strings":["#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108374265","display_name":"Michiel Smid","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michiel Smid","raw_affiliation_strings":["#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"#N#            \u2020 School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5013674788"],"corresponding_institution_ids":["https://openalex.org/I188497080"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07991361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":"5","first_page":"1803","last_page":"1820"},"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9869999885559082,"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/combinatorics","display_name":"Combinatorics","score":0.8891154527664185},{"id":"https://openalex.org/keywords/spanner","display_name":"Spanner","score":0.8407198190689087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6139248609542847},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5986579656600952},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5947554111480713},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45307421684265137},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41875797510147095},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34665125608444214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10650575160980225}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8891154527664185},{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.8407198190689087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6139248609542847},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5986579656600952},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5947554111480713},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45307421684265137},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41875797510147095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34665125608444214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10650575160980225},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070707130","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070707130","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":9,"referenced_works":["https://openalex.org/W1496182974","https://openalex.org/W1505970908","https://openalex.org/W2002041206","https://openalex.org/W2028430839","https://openalex.org/W2054011861","https://openalex.org/W2055488252","https://openalex.org/W2106110423","https://openalex.org/W2145872403","https://openalex.org/W2950657579"],"related_works":["https://openalex.org/W2993304180","https://openalex.org/W4287999588","https://openalex.org/W3082881870","https://openalex.org/W1611446778","https://openalex.org/W2033607935","https://openalex.org/W4377371889","https://openalex.org/W4237934402","https://openalex.org/W4389362338","https://openalex.org/W2113623403","https://openalex.org/W2055932080"],"abstract_inverted_index":{"We":[0,37,81],"address":[1],"the":[2],"following":[3],"problem:":[4],"Given":[5],"a":[6,16,24,30,48,63],"complete":[7,106],"k-partite":[8,107],"geometric":[9,108],"graph":[10],"K":[11,27,51,66],"whose":[12],"vertex":[13],"set":[14,17],"is":[15,79],"of":[18,26,50,65],"n":[19],"points":[20],"in":[21,55,71],"$\\mathbb{R}^d$,":[22],"compute":[23],"spanner":[25],"that":[28,83],"has":[29],"\u201csmall\u201d":[31],"stretch":[32,96],"factor":[33,97],"and":[34,95],"\u201cfew\u201d":[35],"edges.":[36],"present":[38],"two":[39],"algorithms":[40],"for":[41,84,104],"this":[42],"problem.":[43],"The":[44,59,76],"first":[45],"algorithm":[46,61],"computes":[47,62],"$(5+\\epsilon)$-spanner":[49],"with":[52,67,91],"$O(n)$":[53],"edges":[54,70,94],"$O(n\\log":[56,68,92],"n)$":[57,69,74,93],"time.":[58,75],"second":[60],"$(3+\\epsilon)$-spanner":[64],"$O(n":[72],"\\log":[73],"latter":[77],"result":[78],"optimal:":[80],"show":[82],"any":[85],"$2\\leq":[86],"k\\leq":[87],"n-\\Theta(\\sqrt{n\\log":[88],"n})$,":[89],"spanners":[90],"less":[98],"than":[99],"3":[100],"do":[101],"not":[102],"exist":[103],"all":[105],"graphs.":[109]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}