{"id":"https://openalex.org/W1968194367","doi":"https://doi.org/10.1137/s0895480190184811","title":"Extremal Problems in the Construction of Distributed Loop Networks","display_name":"Extremal Problems in the Construction of Distributed Loop Networks","publication_year":1994,"publication_date":"1994-02-01","ids":{"openalex":"https://openalex.org/W1968194367","doi":"https://doi.org/10.1137/s0895480190184811","mag":"1968194367"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480190184811","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480190184811","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/A5101962233","display_name":"D. Frank Hsu","orcid":"https://orcid.org/0000-0003-0468-0843"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D. Frank Hsu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108284194","display_name":"Xing\u2010De Jia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xing-De Jia","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101962233"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0378,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.77979422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"1","first_page":"57","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9944000244140625,"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":0.9944000244140625,"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/T11009","display_name":"Catalysis for Biomass Conversion","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9818000197410583,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.8713369965553284},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8083879351615906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7748979330062866},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.7283886671066284},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7249628901481628},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47193190455436707},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.43371865153312683},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.43252843618392944},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.13485756516456604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0741339921951294}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8713369965553284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8083879351615906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7748979330062866},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.7283886671066284},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7249628901481628},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47193190455436707},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.43371865153312683},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.43252843618392944},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.13485756516456604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0741339921951294},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480190184811","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480190184811","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/W1899309126","https://openalex.org/W1969068850","https://openalex.org/W1982177191","https://openalex.org/W2035468959","https://openalex.org/W2070979794","https://openalex.org/W2077736855"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W1975203667","https://openalex.org/W2370328482","https://openalex.org/W4287882779","https://openalex.org/W2046896701","https://openalex.org/W2265849288","https://openalex.org/W2140169421","https://openalex.org/W1981643426","https://openalex.org/W2905587831","https://openalex.org/W2364040885"],"abstract_inverted_index":{"Let":[0,34],"$G(":[1,47],"N,A":[2,48],")$":[3,12,37,49,86,92],"be":[4,38],"the":[5,39,44,108,119,131],"Cayley":[6],"digraph":[7],"associated":[8],"with":[9,69],"$Z/(":[10],"N":[11,16,41],"and":[13,21,89,118],"A,":[14],"where":[15],"is":[17,23,50,87,93,127],"a":[18,24],"positive":[19],"integer":[20],"A":[22,113],"subset":[25],"of":[26,46,110,133],"$\\{":[27],"1,2,":[28],"\\ldots":[29,65],",N":[30],"-":[31],"1":[32],"\\}$.":[33],"$N(":[35,84,90],"d,k":[36,91],"maximum":[40],"such":[42],"that":[43],"diameter":[45,106],"less":[51],"than":[52],"or":[53],"equal":[54],"to":[55,129],"d":[56],"for":[57,83,95,104],"some":[58],"$A":[59],"=":[60,71],"\\{":[61],"a_1":[62,72],",a_2":[63],",":[64,66],"a_k":[67,78],"\\}$":[68],"$1":[70],"<":[73,75,77],"a_2":[74],"\\cdots":[76],"$.":[79],"An":[80],"exact":[81],"formula":[82],"d,2":[85],"given,":[88],"estimated":[94],"$k":[96],"\\geq":[97],"3$.":[98],"These":[99],"results":[100],"provide":[101],"new":[102],"bounds":[103],"minimal":[105],"in":[107,123],"construction":[109],"loop":[111],"networks.":[112],"relation":[114],"between":[115],"this":[116],"problem":[117,122],"postage":[120],"stamp":[121],"additive":[124],"number":[125],"theory":[126],"established":[128],"enhance":[130],"study":[132],"these":[134],"problems.":[135]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}