{"id":"https://openalex.org/W2041437464","doi":"https://doi.org/10.1137/0214056","title":"Decomposing a Polygon into Simpler Components","display_name":"Decomposing a Polygon into Simpler Components","publication_year":1985,"publication_date":"1985-11-01","ids":{"openalex":"https://openalex.org/W2041437464","doi":"https://doi.org/10.1137/0214056","mag":"2041437464"},"language":"en","primary_location":{"id":"doi:10.1137/0214056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214056","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/A5043506071","display_name":"Julian Keil","orcid":"https://orcid.org/0000-0002-5284-2002"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. Mark Keil","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043506071"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":18.0078,"has_fulltext":false,"cited_by_count":188,"citation_normalized_percentile":{"value":0.9923758,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"799","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9970999956130981,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9861000180244446,"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/monotone-polygon","display_name":"Monotone polygon","score":0.7854986190795898},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.7332884669303894},{"id":"https://openalex.org/keywords/point-in-polygon","display_name":"Point in polygon","score":0.7115526795387268},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.5952979326248169},{"id":"https://openalex.org/keywords/rectilinear-polygon","display_name":"Rectilinear polygon","score":0.582276463508606},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.5612281560897827},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5503763556480408},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5053706765174866},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45740512013435364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4481920599937439},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.446468323469162},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36853042244911194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3330160677433014},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12308362126350403}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7854986190795898},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.7332884669303894},{"id":"https://openalex.org/C59902600","wikidata":"https://www.wikidata.org/wiki/Q1575331","display_name":"Point in polygon","level":3,"score":0.7115526795387268},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.5952979326248169},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.582276463508606},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.5612281560897827},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5503763556480408},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5053706765174866},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45740512013435364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4481920599937439},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.446468323469162},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36853042244911194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3330160677433014},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12308362126350403},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"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":1,"locations":[{"id":"doi:10.1137/0214056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214056","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W79131202","https://openalex.org/W1566622904","https://openalex.org/W1975470983","https://openalex.org/W1981988453","https://openalex.org/W1982182450","https://openalex.org/W1994072439","https://openalex.org/W2004389974","https://openalex.org/W2033775003","https://openalex.org/W2042628505","https://openalex.org/W2045783875","https://openalex.org/W2047940848","https://openalex.org/W2048586177","https://openalex.org/W2049864887","https://openalex.org/W2076834729","https://openalex.org/W2092614653","https://openalex.org/W2104846262","https://openalex.org/W3192672649"],"related_works":["https://openalex.org/W2608536130","https://openalex.org/W2102467404","https://openalex.org/W2466150543","https://openalex.org/W2362048241","https://openalex.org/W2372903818","https://openalex.org/W2389833224","https://openalex.org/W2370449776","https://openalex.org/W2379265227","https://openalex.org/W2381384555","https://openalex.org/W2045509593"],"abstract_inverted_index":{"The":[0,35],"problem":[1],"of":[2,10,58,72,81,83,102,109,117,135],"decomposing":[3,73,103],"a":[4,52,74,104],"polygon":[5,76,106],"into":[6,77,107],"simpler":[7,36],"components":[8,37],"is":[9],"interest":[11],"in":[12,62],"fields":[13],"such":[14],"as":[15],"computational":[16],"geometry,":[17],"syntactic":[18],"pattern":[19],"recognition,":[20],"and":[21,47],"graphics.":[22],"In":[23],"this":[24],"paper":[25],"we":[26,38,91],"consider":[27,39],"decompositions":[28],"which":[29],"do":[30],"not":[31],"introduce":[32],"Steiner":[33],"points.":[34],"are":[40,92,129],"convex":[41],"polygons,":[42,44],"spiral":[43],"star-shaped":[45],"polygons":[46,128],"monotone":[48],"polygons.":[49],"We":[50],"apply":[51],"technique":[53,90],"for":[54,69,99],"improving":[55],"the":[56,70,78,84,88,100,110,115,118,124,127,136],"efficiency":[57],"dynamic":[59],"programming":[60],"algorithms":[61,68,98],"order":[63],"to":[64,94,122,131],"achieve":[65],"polynomial":[66,96],"time":[67,97],"problems":[71,101,137],"simple":[75,105],"minimum":[79],"number":[80],"each":[82,108],"component":[85,111],"types.":[86],"Using":[87],"same":[89],"able":[93],"exhibit":[95],"types":[112],"while":[113],"minimizing":[114],"length":[116],"internal":[119],"edges":[120],"used":[121],"form":[123],"decomposition.":[125],"When":[126],"allowed":[130],"contain":[132],"holes":[133],"many":[134],"become":[138],"NP-hard.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-03-09T08:58:05.943551","created_date":"2025-10-10T00:00:00"}
