{"id":"https://openalex.org/W2167511304","doi":"https://doi.org/10.1142/s0129054109006486","title":"ON SPANNERS OF GEOMETRIC GRAPHS","display_name":"ON SPANNERS OF GEOMETRIC GRAPHS","publication_year":2009,"publication_date":"2009-02-01","ids":{"openalex":"https://openalex.org/W2167511304","doi":"https://doi.org/10.1142/s0129054109006486","mag":"2167511304"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054109006486","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054109006486","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5087003217","display_name":"Joachim Gudmundsson","orcid":"https://orcid.org/0000-0002-6778-7990"},"institutions":[{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"JOACHIM GUDMUNDSSON","raw_affiliation_strings":["National ICT Australia Ltd., Sydney, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National ICT Australia Ltd., Sydney, Australia","institution_ids":["https://openalex.org/I42894916"]}]},{"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":["School of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1703,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92120344,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"01","first_page":"135","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994999766349792,"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":0.8696345090866089},{"id":"https://openalex.org/keywords/spanner","display_name":"Spanner","score":0.8029861450195312},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6826108694076538},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5555289387702942},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5384748578071594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4328767955303192},{"id":"https://openalex.org/keywords/geometric-graph-theory","display_name":"Geometric graph theory","score":0.422066330909729},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.299567848443985},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.23771589994430542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13499847054481506}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8696345090866089},{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.8029861450195312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6826108694076538},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5555289387702942},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5384748578071594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4328767955303192},{"id":"https://openalex.org/C173547177","wikidata":"https://www.wikidata.org/wiki/Q1503271","display_name":"Geometric graph theory","level":5,"score":0.422066330909729},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.299567848443985},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.23771589994430542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13499847054481506},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0},{"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:10.1142/s0129054109006486","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054109006486","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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":15,"referenced_works":["https://openalex.org/W63101354","https://openalex.org/W1505970908","https://openalex.org/W1552092932","https://openalex.org/W1555007779","https://openalex.org/W2002041206","https://openalex.org/W2055488252","https://openalex.org/W2063722406","https://openalex.org/W2069409708","https://openalex.org/W2076639460","https://openalex.org/W2106110423","https://openalex.org/W2506088122","https://openalex.org/W2912257407","https://openalex.org/W4235562408","https://openalex.org/W4245082111","https://openalex.org/W4245662714"],"related_works":["https://openalex.org/W2949889395","https://openalex.org/W2162831161","https://openalex.org/W4297623464","https://openalex.org/W1611446778","https://openalex.org/W229853467","https://openalex.org/W2475249848","https://openalex.org/W4386302423","https://openalex.org/W2167511304","https://openalex.org/W1558884195","https://openalex.org/W187668908"],"abstract_inverted_index":{"Given":[0],"a":[1,12,36,74,90,95],"connected":[2,37,67],"geometric":[3,38,92],"graph":[4,39,69,93],"G,":[5],"we":[6],"consider":[7],"the":[8,17,59,85],"problem":[9,86],"of":[10,14,20,48,87],"constructing":[11],"t-spanner":[13,47,75,96],"G":[15,40,49],"having":[16],"minimum":[18],"number":[19,28],"edges.":[21,54,80],"We":[22,81],"prove":[23,83],"that":[24,45,65,84],"for":[25,111],"every":[26,46,66],"real":[27],"t":[29],"with":[30,41,70,76,97],"[Formula:":[31],"see":[32],"text],":[33],"there":[34],"exists":[35],"n":[42,71],"vertices,":[43],"such":[44],"contains":[50,73,94],"\u03a9(n":[51],"1+1/t":[52],")":[53,79],"This":[55],"bound":[56],"almost":[57],"matches":[58],"known":[60,110],"upper":[61],"bound,":[62],"which":[63],"states":[64],"weighted":[68],"vertices":[72],"O(n":[77],"1+2/(t-1)":[78],"also":[82],"deciding":[88],"whether":[89],"given":[91],"at":[98],"most":[99],"K":[100],"edges":[101],"is":[102],"NP-hard.":[103],"Previously,":[104],"this":[105],"NP-hardness":[106],"result":[107],"was":[108],"only":[109],"non-geometric":[112],"graphs.":[113]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}