{"id":"https://openalex.org/W2071945466","doi":"https://doi.org/10.1137/0217057","title":"An Approximation Scheme for Finding Steiner Trees with Obstacles","display_name":"An Approximation Scheme for Finding Steiner Trees with Obstacles","publication_year":1988,"publication_date":"1988-10-01","ids":{"openalex":"https://openalex.org/W2071945466","doi":"https://doi.org/10.1137/0217057","mag":"2071945466"},"language":"en","primary_location":{"id":"doi:10.1137/0217057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217057","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/A5005781105","display_name":"J. Scott Provan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. Scott Provan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005781105"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5404,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.85663082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"5","first_page":"920","last_page":"934"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T12546","display_name":"Smart Parking Systems Research","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.9587412476539612},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.781287431716919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7091629505157471},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6718209385871887},{"id":"https://openalex.org/keywords/k-minimum-spanning-tree","display_name":"k-minimum spanning tree","score":0.6120103001594543},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5870541930198669},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5419519543647766},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.536787211894989},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4738923907279968},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4715286195278168},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.45100557804107666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4135262072086334},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.35468950867652893},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.21353408694267273},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.138456791639328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13784438371658325},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07861748337745667},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06821262836456299}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.9587412476539612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.781287431716919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7091629505157471},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6718209385871887},{"id":"https://openalex.org/C202750272","wikidata":"https://www.wikidata.org/wiki/Q6322849","display_name":"k-minimum spanning tree","level":5,"score":0.6120103001594543},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5870541930198669},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5419519543647766},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.536787211894989},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4738923907279968},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4715286195278168},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.45100557804107666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4135262072086334},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.35468950867652893},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.21353408694267273},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.138456791639328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13784438371658325},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07861748337745667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06821262836456299},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0217057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217057","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":25,"referenced_works":["https://openalex.org/W628736642","https://openalex.org/W1528622396","https://openalex.org/W1965701993","https://openalex.org/W1976021853","https://openalex.org/W1990488643","https://openalex.org/W1996668544","https://openalex.org/W2016082605","https://openalex.org/W2022150791","https://openalex.org/W2030261330","https://openalex.org/W2040444410","https://openalex.org/W2042477130","https://openalex.org/W2048013200","https://openalex.org/W2049637478","https://openalex.org/W2060380213","https://openalex.org/W2081777693","https://openalex.org/W2085242823","https://openalex.org/W2086709935","https://openalex.org/W2115616619","https://openalex.org/W2132087752","https://openalex.org/W2150855695","https://openalex.org/W2156503228","https://openalex.org/W2163178194","https://openalex.org/W2163668690","https://openalex.org/W2169528473","https://openalex.org/W2172222998"],"related_works":["https://openalex.org/W1980288485","https://openalex.org/W1998126097","https://openalex.org/W2367195720","https://openalex.org/W974563791","https://openalex.org/W2739242419","https://openalex.org/W1595291551","https://openalex.org/W4244816249","https://openalex.org/W1968497507","https://openalex.org/W2183636263","https://openalex.org/W3184075718"],"abstract_inverted_index":{"We":[0,32,57],"consider":[1],"the":[2,30,35,53,66,88,126,130,144],"problem":[3,79,148],"of":[4,15,38,48,91,111,117],"constructing":[5],"a":[6,11,20,44,76,81,96,108],"Steiner":[7,54,67,77,131,145],"minimal":[8,55,68,132,146],"tree":[9,69,78,133,147],"connecting":[10],"given":[12,122],"set":[13],"K":[14,39,86,102],"points":[16,113],"and":[17,87,114,138],"lying":[18],"inside":[19],"polygonally":[21],"bounded,":[22],"not":[23],"necessarily":[24],"simply":[25],"connected":[26],"region":[27,127],"R":[28,49,71],"in":[29,40,70,128],"plane.":[31],"first":[33],"define":[34],"path-convex":[36,89],"hull":[37,90],"R,":[41],"which":[42,123,129,139],"is":[43,103,134],"\u201csufficiently":[45],"small\u201d":[46],"subregion":[47],"guaranteed":[50],"to":[51,64,75,105,136],"contain":[52],"tree.":[56],"then":[58],"give":[59],"an":[60],"$\\varepsilon":[61],"$-approximation":[62],"scheme":[63,100],"find":[65],"by":[72],"reducing":[73],"it":[74],"on":[80,107],"\u201cvisibility":[82],"graph\u201d":[83],"associated":[84],"with":[85],"R.":[92,118],"This":[93],"will":[94],"be":[95],"fully":[97],"polynomial":[98],"approximation":[99],"when":[101],"restricted":[104],"lie":[106],"small":[109],"number":[110],"interior":[112],"boundary":[115],"polygons":[116],"Several":[119],"techniques":[120],"are":[121],"further":[124],"reduce":[125],"known":[135,141],"lie,":[137],"extend":[140],"results":[142],"for":[143],"without":[149],"obstacles.":[150]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
