{"id":"https://openalex.org/W2133962824","doi":"https://doi.org/10.1137/0213014","title":"On the Complexity of Some Common Geometric Location Problems","display_name":"On the Complexity of Some Common Geometric Location Problems","publication_year":1984,"publication_date":"1984-02-01","ids":{"openalex":"https://openalex.org/W2133962824","doi":"https://doi.org/10.1137/0213014","mag":"2133962824"},"language":"en","primary_location":{"id":"doi:10.1137/0213014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213014","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/A5019904083","display_name":"Nimrod Megiddo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nimrod Megiddo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047833204","display_name":"Kenneth J. Supowit","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kenneth J. Supowit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019904083"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.6252,"has_fulltext":false,"cited_by_count":670,"citation_normalized_percentile":{"value":0.98381295,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"13","issue":"1","first_page":"182","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9962999820709229,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9934999942779541,"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/combinatorics","display_name":"Combinatorics","score":0.650193989276886},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6374298334121704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6274729371070862},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5943151116371155},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5645491480827332},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5640935301780701},{"id":"https://openalex.org/keywords/1-center-problem","display_name":"1-center problem","score":0.52220219373703},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5078805088996887},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.46365293860435486},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.4549926221370697},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.43510979413986206},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40183427929878235},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3169906735420227},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24001064896583557},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15359875559806824}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.650193989276886},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6374298334121704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6274729371070862},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5943151116371155},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5645491480827332},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5640935301780701},{"id":"https://openalex.org/C50524431","wikidata":"https://www.wikidata.org/wiki/Q4545814","display_name":"1-center problem","level":3,"score":0.52220219373703},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5078805088996887},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.46365293860435486},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.4549926221370697},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.43510979413986206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40183427929878235},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3169906735420227},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24001064896583557},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15359875559806824},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0213014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213014","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.142.2364","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.2364","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~megiddo/pdf/complexity%20of%20common%20geometric%20location%20problems.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W113434742","https://openalex.org/W1984953641","https://openalex.org/W2007610503","https://openalex.org/W2011039300","https://openalex.org/W2042032955","https://openalex.org/W2055569927","https://openalex.org/W2066194644","https://openalex.org/W2074290597","https://openalex.org/W2079886069","https://openalex.org/W2139594840","https://openalex.org/W2141178123","https://openalex.org/W2570178494","https://openalex.org/W4239852074"],"related_works":["https://openalex.org/W276709744","https://openalex.org/W2173317315","https://openalex.org/W2074682523","https://openalex.org/W4248426730","https://openalex.org/W1998932824","https://openalex.org/W2006514056","https://openalex.org/W2476148062","https://openalex.org/W1509863433","https://openalex.org/W2499461890","https://openalex.org/W2057791178"],"abstract_inverted_index":{"Given":[0],"n":[1],"demand":[2,29,48],"points":[3,15,49],"in":[4,17],"the":[5,7,18,24,43,59,62,68,71,87],"plane,":[6],"p-center":[8,60,88],"problem":[9,39],"is":[10,40,82],"to":[11,22,31,41,50,66,85],"find":[12],"p":[13],"supply":[14,35,54],"(anywhere":[16],"plane)":[19],"so":[20],"as":[21],"minimize":[23,42],"maximum":[25],"distance":[26],"from":[27,47,95],"a":[28],"point":[30],"its":[32],"respective":[33,52],"nearest":[34,53],"point.":[36],"The":[37,92],"p-median":[38,63],"sum":[44],"of":[45],"distances":[46],"their":[51],"points.":[55],"We":[56],"prove":[57,79],"that":[58,80],"and":[61,70],"problems":[64,89],"relative":[65],"both":[67],"Euclidean":[69],"rectilinear":[72],"metrics":[73],"are":[74,94],"NP-hard.":[75],"In":[76],"fact,":[77],"we":[78],"it":[81],"NP-hard":[83],"even":[84],"approximate":[86],"sufficiently":[90],"closely.":[91],"reductions":[93],"3-satisfiability.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":34},{"year":2021,"cited_by_count":43},{"year":2020,"cited_by_count":29},{"year":2019,"cited_by_count":45},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":29},{"year":2016,"cited_by_count":27},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":28},{"year":2013,"cited_by_count":26},{"year":2012,"cited_by_count":24}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}