{"id":"https://openalex.org/W1552020712","doi":"https://doi.org/10.1016/s0166-218x(00)00280-8","title":"Lower bounds for computing geometric spanners and approximate shortest paths","display_name":"Lower bounds for computing geometric spanners and approximate shortest paths","publication_year":2001,"publication_date":"2001-06-01","ids":{"openalex":"https://openalex.org/W1552020712","doi":"https://doi.org/10.1016/s0166-218x(00)00280-8","mag":"1552020712"},"language":"en","primary_location":{"id":"doi:10.1016/s0166-218x(00)00280-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0166-218x(00)00280-8","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://www.cccg.ca/proceedings/1996/cccg1996_0027.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060901632","display_name":"Danny Z. Chen","orcid":"https://orcid.org/0000-0001-6565-2884"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Danny Z. Chen","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA","Department of Computer Science & Engineering University of Notre Dame Notre Dame IN 46556 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Computer Science & Engineering University of Notre Dame Notre Dame IN 46556 USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002203026","display_name":"Gautam Das","orcid":"https://orcid.org/0000-0002-4627-9065"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Gautam Das","raw_affiliation_strings":["Math Sciences Department, The University of Memphis, Memphis, TN 38152, USA","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Math Sciences Department, The University of Memphis, Memphis, TN 38152, USA","institution_ids":["https://openalex.org/I94658018"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108374265","display_name":"Michiel Smid","orcid":null},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michiel Smid","raw_affiliation_strings":["Department of Computer Science, University of Magdeburg, D-39106 Magdeburg, Germany","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Magdeburg, D-39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5108374265"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210138551"],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12401353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"110","issue":"2-3","first_page":"151","last_page":"167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9969000220298767,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9930999875068665,"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":0.709608256816864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6268965005874634},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5289899110794067},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.5192082524299622},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5101497769355774},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.492525190114975},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4916866421699524},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4789081811904907},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.468142569065094},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4482281506061554},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.44444209337234497},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4427068531513214},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44253793358802795},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4287390112876892},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24618524312973022},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19085624814033508},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.17956075072288513},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07526436448097229}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.709608256816864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6268965005874634},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5289899110794067},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.5192082524299622},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5101497769355774},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.492525190114975},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4916866421699524},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4789081811904907},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.468142569065094},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4482281506061554},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.44444209337234497},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4427068531513214},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44253793358802795},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4287390112876892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24618524312973022},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19085624814033508},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.17956075072288513},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07526436448097229},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":7,"locations":[{"id":"doi:10.1016/s0166-218x(00)00280-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0166-218x(00)00280-8","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:pure.mpg.de:item_1331701","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-AB7D-4","pdf_url":"http://www.cccg.ca/proceedings/1996/cccg1996_0027.pdf","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 8th Canadian Conference on Computational Geometry","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.9566","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.9566","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://isgwww.cs.uni-magdeburg.de/~michiel/lowerspanner.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.6268","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.6268","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hypatia.dcs.qmw.ac.uk/data/uk/dcs.kcl.ac.uk/tr96-09.ps.gz","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:517750","is_oa":false,"landing_page_url":"http://edoc.mpg.de/517750","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"8th Canadian Conference on Computing, Carleton, 155-160 (1996)","raw_type":"Conference-Paper"},{"id":"mag:1552020712","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1331701","pdf_url":null,"source":{"id":"https://openalex.org/S4306533943","display_name":"Untitled Event","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Untitled Event","raw_type":null},{"id":"mag:1553270684","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/cccg/cccg1996.html#ChenDS96","pdf_url":null,"source":{"id":"https://openalex.org/S4306417878","display_name":"Canadian Conference on Computational Geometry","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Canadian Conference on Computational Geometry","raw_type":null}],"best_oa_location":{"id":"pmh:oai:pure.mpg.de:item_1331701","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-AB7D-4","pdf_url":"http://www.cccg.ca/proceedings/1996/cccg1996_0027.pdf","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 8th Canadian Conference on Computational Geometry","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1552020712.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1481010420","https://openalex.org/W1992320342","https://openalex.org/W2014843742","https://openalex.org/W2036114412","https://openalex.org/W2055488252","https://openalex.org/W2058510050","https://openalex.org/W2059985428","https://openalex.org/W2063372577","https://openalex.org/W2106110423","https://openalex.org/W2108741984","https://openalex.org/W2139391136","https://openalex.org/W6605561933","https://openalex.org/W6632219655"],"related_works":["https://openalex.org/W2052373622","https://openalex.org/W2950077120","https://openalex.org/W2963551506","https://openalex.org/W2582648736","https://openalex.org/W1975248037","https://openalex.org/W2161408306","https://openalex.org/W2223620343","https://openalex.org/W2043285556","https://openalex.org/W1980197133","https://openalex.org/W1648876443","https://openalex.org/W3105802762","https://openalex.org/W2124012370","https://openalex.org/W3000110732","https://openalex.org/W2067305605","https://openalex.org/W1719465442","https://openalex.org/W2075927382","https://openalex.org/W3200681452","https://openalex.org/W2100366694","https://openalex.org/W2591314370","https://openalex.org/W2074455653"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
