{"id":"https://openalex.org/W2139349113","doi":"https://doi.org/10.1002/net.3230250205","title":"Simple heuristics for unit disk graphs","display_name":"Simple heuristics for unit disk graphs","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2139349113","doi":"https://doi.org/10.1002/net.3230250205","mag":"2139349113"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230250205","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230250205","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5020293284","display_name":"Madhav Marathe","orcid":"https://orcid.org/0000-0003-1653-0658"},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. V. Marathe","raw_affiliation_strings":["Department of Computer Science, University at Albany-SUNY, Albany, New York 12222","Department of Computer Science, University at Albany\u2010SUNY, Albany, New York 12222"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University at Albany-SUNY, Albany, New York 12222","institution_ids":["https://openalex.org/I392282"]},{"raw_affiliation_string":"Department of Computer Science, University at Albany\u2010SUNY, Albany, New York 12222","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017645609","display_name":"Heinz Breu","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"H. Breu","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4","Department of Computer Science, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z4#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z4#TAB#","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086835651","display_name":"Harry B. Hunt","orcid":null},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. B. Hunt","raw_affiliation_strings":["Department of Computer Science, University of Albany-SUNY, Albany, New York 12222"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Albany-SUNY, Albany, New York 12222","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086740853","display_name":"S. S. Ravi","orcid":"https://orcid.org/0000-0002-0893-4364"},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. S. Ravi","raw_affiliation_strings":["Department of Computer Science, University of Albany-SUNY, Albany, New York 12222"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Albany-SUNY, Albany, New York 12222","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009388396","display_name":"Daniel J. Rosenkrantz","orcid":"https://orcid.org/0000-0002-7044-0197"},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. J. Rosenkrantz","raw_affiliation_strings":["Department of Computer Science, University of Albany-SUNY, Albany, New York 12222"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Albany-SUNY, Albany, New York 12222","institution_ids":["https://openalex.org/I392282"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5020293284"],"corresponding_institution_ids":["https://openalex.org/I392282"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":3.7509,"has_fulltext":false,"cited_by_count":493,"citation_normalized_percentile":{"value":0.9322884,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"25","issue":"2","first_page":"59","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9954000115394592,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/unit-disk-graph","display_name":"Unit disk graph","score":0.7981849312782288},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.7965157628059387},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6709959506988525},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.6694017648696899},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.590129554271698},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.5722835063934326},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5014448165893555},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4829387068748474},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.47118711471557617},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.42399269342422485},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38793984055519104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36088863015174866},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.2885109782218933},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21037158370018005},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.18685373663902283}],"concepts":[{"id":"https://openalex.org/C130184317","wikidata":"https://www.wikidata.org/wiki/Q3115549","display_name":"Unit disk graph","level":4,"score":0.7981849312782288},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.7965157628059387},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6709959506988525},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.6694017648696899},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.590129554271698},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.5722835063934326},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5014448165893555},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4829387068748474},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.47118711471557617},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.42399269342422485},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38793984055519104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36088863015174866},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2885109782218933},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21037158370018005},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.18685373663902283},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.0},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/net.3230250205","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230250205","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.2281","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.2281","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/9409226v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.41.1165","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.1165","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwc3.lanl.gov/~madhav/pubs.d/udisk-networks.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W182747812","https://openalex.org/W1513353427","https://openalex.org/W1536050932","https://openalex.org/W1557755441","https://openalex.org/W1572977974","https://openalex.org/W1945376352","https://openalex.org/W1975512711","https://openalex.org/W1982378203","https://openalex.org/W1995990042","https://openalex.org/W2000419386","https://openalex.org/W2006632549","https://openalex.org/W2011039300","https://openalex.org/W2013415302","https://openalex.org/W2040924621","https://openalex.org/W2053439155","https://openalex.org/W2056979696","https://openalex.org/W2063572899","https://openalex.org/W2077783414","https://openalex.org/W2079473728","https://openalex.org/W2090487839","https://openalex.org/W2091112956","https://openalex.org/W2092958336","https://openalex.org/W2100961486","https://openalex.org/W2104170004","https://openalex.org/W2122858887","https://openalex.org/W2143391442","https://openalex.org/W2143474538","https://openalex.org/W2148102331","https://openalex.org/W2166858292","https://openalex.org/W4285719527","https://openalex.org/W4293259454","https://openalex.org/W4299866835"],"related_works":["https://openalex.org/W4283803822","https://openalex.org/W2157783000","https://openalex.org/W2963009577","https://openalex.org/W4287117052","https://openalex.org/W2788975631","https://openalex.org/W2966902162","https://openalex.org/W2903402681","https://openalex.org/W3176308333","https://openalex.org/W4206705200","https://openalex.org/W1968027460"],"abstract_inverted_index":{"Abstract":[0],"Unit":[1],"disk":[2,32,66,78],"graphs":[3,6,103,113,119],"are":[4,82],"intersection":[5,102,112,118],"of":[7,9,25,62,76,90,94,104,106,114,120],"circles":[8,105],"unit":[10,31,65,77],"radius":[11],"in":[12,85,109],"the":[13,87,91,110],"plane.":[14],"We":[15,50],"present":[16,52],"simple":[17],"and":[18,46,117],"provably":[19],"good":[20],"heuristics":[21,69],"for":[22,64],"a":[23,59,73],"number":[24],"classical":[26],"NP\u2010hard":[27],"optimization":[28],"problems":[29,35],"on":[30],"graphs.":[33,67,79],"The":[34],"considered":[36],"include":[37],"maximum":[38],"independent":[39],"set,":[40],"minimum":[41,44,47],"vertex":[42],"cover,":[43],"coloring,":[45],"dominating":[48],"set.":[49],"also":[51],"an":[53],"on\u2010line":[54],"coloring":[55],"heuristic":[56],"which":[57],"achieves":[58],"competitive":[60],"ratio":[61],"6":[63],"Our":[68],"do":[70],"not":[71],"need":[72],"geometric":[74],"representation":[75],"Geometric":[80],"representations":[81],"used":[83],"only":[84],"establishing":[86],"performance":[88],"guarantees":[89],"heuristics.":[92],"Several":[93],"our":[95],"approximation":[96],"algorithms":[97],"can":[98],"be":[99],"extended":[100],"to":[101],"arbitrary":[107],"radii":[108],"plane,":[111],"regular":[115,123],"polygons,":[116],"higher":[121],"dimensional":[122],"objects.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":20},{"year":2013,"cited_by_count":26},{"year":2012,"cited_by_count":25}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}