{"id":"https://openalex.org/W1996164900","doi":"https://doi.org/10.1002/net.3230150403","title":"Probabilistic partitioning algorithms for the rectilinear steiner problem","display_name":"Probabilistic partitioning algorithms for the rectilinear steiner problem","publication_year":1985,"publication_date":"1985-12-01","ids":{"openalex":"https://openalex.org/W1996164900","doi":"https://doi.org/10.1002/net.3230150403","mag":"1996164900"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230150403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230150403","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/A5081681841","display_name":"J\u00e1nos Koml\u00f3s","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J\u00e1nos Koml\u00f3s","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, CA 92093","Dept. of Mathematics, University of California, San Diego, La Jolla, CA 92093"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, CA 92093","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Dept. of Mathematics, University of California, San Diego, La Jolla, CA 92093","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042563610","display_name":"Man\u2010Tak Shing","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. T. Shing","raw_affiliation_strings":["Department of Computer Science, University of California, Santa Barbara, CA 93106"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":1.6487,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.81466035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"4","first_page":"413","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9965000152587891,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.8848739862442017},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8250604867935181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6735327243804932},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5811440944671631},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5761559009552002},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4349668025970459},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42906510829925537},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.369597464799881},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1750088632106781}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.8848739862442017},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8250604867935181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6735327243804932},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5811440944671631},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5761559009552002},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4349668025970459},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42906510829925537},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.369597464799881},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1750088632106781},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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:10.1002/net.3230150403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230150403","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W115590081","https://openalex.org/W1655990431","https://openalex.org/W1965680834","https://openalex.org/W1971164886","https://openalex.org/W1976925751","https://openalex.org/W1996668544","https://openalex.org/W2020112047","https://openalex.org/W2064086982","https://openalex.org/W2069712919","https://openalex.org/W2082293426","https://openalex.org/W2143037347","https://openalex.org/W2161014683","https://openalex.org/W2168570149","https://openalex.org/W2318153728","https://openalex.org/W2590190460","https://openalex.org/W2767753875","https://openalex.org/W4302399279"],"related_works":["https://openalex.org/W2161182859","https://openalex.org/W2118320476","https://openalex.org/W1503036335","https://openalex.org/W2025658531","https://openalex.org/W4244816249","https://openalex.org/W2115973883","https://openalex.org/W2739242419","https://openalex.org/W1585318792","https://openalex.org/W28092394","https://openalex.org/W777204940"],"abstract_inverted_index":{"Abstract":[0],"Based":[1],"on":[2],"the":[3,16,23,28,54,65,77,102,150],"probabilistic":[4],"approach":[5],"introduced":[6],"by":[7,85],"Karp":[8],"[14],":[9],"we":[10],"present":[11],"two":[12],"partitioning":[13],"algorithms":[14,31],"for":[15,47,64,95],"approximate":[17],"solution":[18],"of":[19,22,35,158],"large":[20],"instances":[21],"rectilinear":[24,44,61,88,122,172],"Steiner":[25,45,62,89,123,173],"problem":[26],"in":[27,106],"plane.":[29],"The":[30],"subdivide":[32],"a":[33,42,59,86,121,171],"set":[34],"given":[36,66,72,97],"points":[37],"into":[38],"small":[39,49],"groups,":[40],"construct":[41],"minimum":[43,87],"tree":[46,63,90,124,174],"each":[48],"group,":[50],"and":[51,83,119,167],"then":[52],"patch":[53],"subtrees":[55],"together":[56],"to":[57],"form":[58],"near\u2010optimum":[60],"points.":[67],"Suppose":[68],"there":[69],"are":[70],"n":[71,112,114,116,146,165,196],"points,":[73],"uniformly":[74],"distributed":[75],"over":[76],"unit":[78],"square":[79],"[0,1]":[80,82],"\u00d7":[81],"spanned":[84],"T":[91,125,175],"o":[92],".":[93],"Then":[94],"any":[96],"integer":[98],"t":[99,110,163],"&gt;":[100],"0,":[101],"first":[103],"algorithm":[104,152],"runs":[105],"O(":[107],"f":[108],"(":[109,160,162],")":[111,117,164,166],"+":[113,136,186],"log":[115],"time":[118,157],"produces":[120,170],"1":[126,135,144,185,194],"such":[127,177],"that":[128,178],"\\documentclass{article}\\pagestyle{empty}\\begin{document}$":[129,179],"\\left({|T_1":[130],"|/|T_0":[131,181],"|}":[132,182],"\\right)":[133,139,183,189],"\\le":[134,184],"O\\left({\\sqrt":[137,187],"{1/t}}":[138,188],"$\\end{document}":[140,190],"with":[141,191],"probability":[142,192],"approaching":[143,193],"as":[145,195],"\u2192":[147,197],"\u221e,":[148],"while":[149],"second":[151],"has":[153],"an":[154],"expected":[155],"running":[156],"O":[159],"g":[161],"it":[168],"also":[169],"2":[176],"\\left({|T_2":[180],"\u221e.":[198]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
