{"id":"https://openalex.org/W2058673623","doi":"https://doi.org/10.1137/0405020","title":"Three-Stage Generalized Connectors","display_name":"Three-Stage Generalized Connectors","publication_year":1992,"publication_date":"1992-05-01","ids":{"openalex":"https://openalex.org/W2058673623","doi":"https://doi.org/10.1137/0405020","mag":"2058673623"},"language":"en","primary_location":{"id":"doi:10.1137/0405020","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405020","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5068875104","display_name":"Richard M. Karp","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Richard M. Karp","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068875104"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.22185629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"2","first_page":"259","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9977999925613403,"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":0.996999979019165,"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/correctness","display_name":"Correctness","score":0.7236831784248352},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7171647548675537},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5861101746559143},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.573369562625885},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5628493428230286},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4760151505470276},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4454965591430664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35073816776275635},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34916532039642334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34880542755126953},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3469383418560028},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09208187460899353}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7236831784248352},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7171647548675537},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5861101746559143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.573369562625885},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5628493428230286},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4760151505470276},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4454965591430664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35073816776275635},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34916532039642334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34880542755126953},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3469383418560028},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09208187460899353},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0405020","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405020","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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":6,"referenced_works":["https://openalex.org/W1987347501","https://openalex.org/W2047528205","https://openalex.org/W2092946387","https://openalex.org/W2155859297","https://openalex.org/W2168961449","https://openalex.org/W2170198451"],"related_works":["https://openalex.org/W3008339103","https://openalex.org/W2404647514","https://openalex.org/W1667647204","https://openalex.org/W4247536566","https://openalex.org/W55831818","https://openalex.org/W1604988569","https://openalex.org/W1497573972","https://openalex.org/W2071659383","https://openalex.org/W1846253165","https://openalex.org/W2124122503"],"abstract_inverted_index":{"An":[0],"acyclic":[1],"directed":[2],"network":[3,90],"with":[4],"n":[5,217],"sources":[6],"and":[7,49,53,77,218],"m":[8,219],"sinks":[9],"is":[10,70,85,91,113,136],"called":[11],"a":[12,55,88,92,100,199,203],"generalized":[13,66,93,224],"connector":[14,94],"if,":[15],"for":[16,162],"any":[17],"request":[18],"pattern":[19],"in":[20,62,99,130,146,175],"which":[21],"each":[22],"sink":[23],"asks":[24],"to":[25,28],"be":[26,39],"connected":[27],"some":[29],"source,":[30],"the":[31,73,116,125,133,141,144,157,163,170,173,190,208,220],"required":[32],"configuration":[33],"of":[34,47,57,79,106,118,127,143,167,172,207,210,216],"noninterfering":[35],"connecting":[36],"paths":[37],"can":[38],"set":[40],"up.":[41],"This":[42,68],"paper":[43],"presents":[44],"new":[45],"families":[46,64],"two-":[48],"three-stage":[50,223],"connection":[51],"networks":[52,61],"gives":[54],"method":[56,69,76],"establishing":[58],"that":[59,87,96,115,156],"particular":[60],"these":[63,119,151,211],"are":[65,105,121,159,177,183,228],"connectors.":[67],"based":[71],"on":[72],"Erd\u00f6s":[74],"probabilistic":[75],"consists":[78],"two":[80],"steps:":[81],"1.":[82],"First":[83],"it":[84,112],"proven":[86],"given":[89],"provided":[95],"certain":[97,214],"events":[98,120,145,174],"probability":[101,191],"space":[102,192],"$\\Omega":[103,193],"$":[104],"sufficiently":[107,123],"low":[108],"probability.":[109],"2.":[110],"Then":[111],"shown":[114],"probabilities":[117,142,171],"indeed":[122],"small.For":[124],"family":[126],"designs":[128,158,166],"presented":[129],"Section":[131,168],"5,":[132],"second":[134],"step":[135],"accomplished":[137],"by":[138,185],"explicitly":[139],"calculating":[140],"question,":[147],"using":[148],"dynamic":[149],"programming;":[150],"calculations":[152],"provide":[153],"rigorous":[154],"proofs":[155],"correct.":[160],"However,":[161],"more":[164],"economical":[165],"6,":[169],"question":[176],"not":[178],"calculated":[179],"exactly,":[180],"but":[181],"instead":[182],"estimated":[184],"drawing":[186],"pseudo-random":[187],"samples":[188],"from":[189],"$.":[194],"Thus,":[195],"we":[196],"have":[197],"only":[198],"\u201cstatistical":[200],"proof\u201d":[201],"(albeit":[202],"very":[204],"convincing":[205],"one)":[206],"correctness":[209],"designs.":[212],"For":[213],"choices":[215],"most":[221],"efficient":[222],"connectors":[225],"currently":[226],"known":[227],"obtained.":[229]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
