{"id":"https://openalex.org/W2004151341","doi":"https://doi.org/10.1137/100791506","title":"Terrain Guarding is NP-Hard","display_name":"Terrain Guarding is NP-Hard","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2004151341","doi":"https://doi.org/10.1137/100791506","mag":"2004151341"},"language":"en","primary_location":{"id":"doi:10.1137/100791506","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100791506","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/A5003376019","display_name":"James King","orcid":"https://orcid.org/0000-0001-8825-0183"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"James King","raw_affiliation_strings":["School of Computer Science, McGill University,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University,","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024865139","display_name":"Erik Krohn","orcid":"https://orcid.org/0000-0002-5832-8135"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erik Krohn","raw_affiliation_strings":["Department of Computer Science, University of Iowa,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Iowa,","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.8792,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.9694078,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"40","issue":"5","first_page":"1316","last_page":"1339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9950000047683716,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/terrain","display_name":"Terrain","score":0.9237215518951416},{"id":"https://openalex.org/keywords/guard","display_name":"Guard (computer science)","score":0.6299644708633423},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5083984732627869},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.48962241411209106},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48122620582580566},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45333606004714966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4275059700012207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34375423192977905},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13487663865089417},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.12415355443954468},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.07129669189453125}],"concepts":[{"id":"https://openalex.org/C161840515","wikidata":"https://www.wikidata.org/wiki/Q186131","display_name":"Terrain","level":2,"score":0.9237215518951416},{"id":"https://openalex.org/C141141315","wikidata":"https://www.wikidata.org/wiki/Q2379942","display_name":"Guard (computer science)","level":2,"score":0.6299644708633423},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5083984732627869},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.48962241411209106},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48122620582580566},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45333606004714966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4275059700012207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34375423192977905},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13487663865089417},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.12415355443954468},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.07129669189453125},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/100791506","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100791506","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:10.1.1.159.1130","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.1130","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.mcgill.ca/~jking/papers/king_krohn_terrain_np-hard.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.215.7606","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.215.7606","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.siam.org/proceedings/soda/2010/SODA10_128_kingj.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.3137","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.3137","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.jking.ca/papers/king_krohn_terrain_np-hard_journal.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1981988453","https://openalex.org/W1987374783","https://openalex.org/W1999396007","https://openalex.org/W2063442090","https://openalex.org/W2066577300","https://openalex.org/W2079577476","https://openalex.org/W2105739218","https://openalex.org/W2110033738","https://openalex.org/W2116909526","https://openalex.org/W2121601978","https://openalex.org/W2164603914"],"related_works":["https://openalex.org/W1992962589","https://openalex.org/W3032871857","https://openalex.org/W1743191351","https://openalex.org/W3104633800","https://openalex.org/W3023567978","https://openalex.org/W3044778482","https://openalex.org/W3040494141","https://openalex.org/W4384026392","https://openalex.org/W1977229594","https://openalex.org/W2072400776"],"abstract_inverted_index":{"A":[0],"set":[1,67],"G":[2],"of":[3,85],"points":[4,35],"on":[5,24,36],"a":[6,30,64,74,92],"terrain,":[7],"also":[8],"known":[9],"as":[10],"an":[11],"x-monotone":[12],"polygonal":[13],"chain,":[14],"is":[15,27,51,88],"said":[16],"to":[17],"guard":[18],"the":[19,25,37,46,55,69,82,103],"terrain":[20,26,38,59],"if":[21,42,45],"every":[22],"point":[23,31],"seen":[28],"by":[29],"in":[32],"G.":[33],"Two":[34],"see":[39],"each":[40],"other":[41],"and":[43,96],"only":[44],"line":[47],"segment":[48],"between":[49],"them":[50],"never":[52],"strictly":[53],"below":[54],"terrain.":[56,72],"The":[57],"minimum":[58,65],"guarding":[60,66],"problem":[61,87,95],"asks":[62],"for":[63,68,102],"given":[70],"input":[71],"Using":[73],"reduction":[75],"from":[76],"PLANAR":[77],"3-SAT":[78],"we":[79],"prove":[80],"that":[81],"decision":[83],"version":[84],"this":[86],"NP-hard.":[89],"This":[90],"solves":[91],"significant":[93],"open":[94],"complements":[97],"recent":[98],"positive":[99],"approximability":[100],"results":[101],"optimization":[104],"problem.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}