{"id":"https://openalex.org/W2162314742","doi":"https://doi.org/10.37236/1695","title":"Optimal Double-Loop Networks with Non-Unit Steps","display_name":"Optimal Double-Loop Networks with Non-Unit Steps","publication_year":2003,"publication_date":"2003-01-06","ids":{"openalex":"https://openalex.org/W2162314742","doi":"https://doi.org/10.37236/1695","mag":"2162314742"},"language":"en","primary_location":{"id":"doi:10.37236/1695","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1695","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043672512","display_name":"F. Aguil\u00f3-Gost","orcid":"https://orcid.org/0000-0003-1572-8486"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"F. Aguil\u00f3","raw_affiliation_strings":["Dept. de Matem\u00e0tica Aplicada IV Universitat Polit\u00e8cnica de Catalunya C/. Jordi Girona 1-3 08034 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. de Matem\u00e0tica Aplicada IV Universitat Polit\u00e8cnica de Catalunya C/. Jordi Girona 1-3 08034 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035993343","display_name":"Ester Sim\u00f3 Mezquita","orcid":"https://orcid.org/0000-0003-4587-7028"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. Sim\u00f3","raw_affiliation_strings":["Dept. de Matem\u00e0tica Aplicada IV Universitat Polit\u00e8cnica de Catalunya C/. Jordi Girona 1-3 08034 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. de Matem\u00e0tica Aplicada IV Universitat Polit\u00e8cnica de Catalunya C/. Jordi Girona 1-3 08034 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112787243","display_name":"Marisa Zaragoz\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Zaragoz\u00e1","raw_affiliation_strings":["Dept. de Matem\u00e0tica Aplicada IV Universitat Polit\u00e8cnica de Catalunya C/. Jordi Girona 1-3 08034 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Dept. de Matem\u00e0tica Aplicada IV Universitat Polit\u00e8cnica de Catalunya C/. Jordi Girona 1-3 08034 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043672512"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":0.2483,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67758621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"1","first_page":null,"last_page":null},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11476","display_name":"Graph theory and applications","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8485594391822815},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8018917441368103},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.6612353324890137},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4688504636287689},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4216476380825043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38931071758270264}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8485594391822815},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8018917441368103},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.6612353324890137},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4688504636287689},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4216476380825043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38931071758270264},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1695","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1695","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.10.4036","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.4036","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PDF/v10i1r2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.9.4292","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.4292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PostScriptfiles/v9i1r47.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1695","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1695","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2631452109","display_name":null,"funder_award_id":"(ERDF)","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2162314742.pdf","grobid_xml":"https://content.openalex.org/works/W2162314742.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1576757684","https://openalex.org/W1899309126","https://openalex.org/W1964104809","https://openalex.org/W1979376805","https://openalex.org/W2015987608","https://openalex.org/W2022995666","https://openalex.org/W2030802892","https://openalex.org/W2064965043","https://openalex.org/W2066957322","https://openalex.org/W2077736855","https://openalex.org/W2082572337","https://openalex.org/W2094613978","https://openalex.org/W2125732536","https://openalex.org/W2137347071","https://openalex.org/W2805312312","https://openalex.org/W4243817294"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W2921632378","https://openalex.org/W1975203667","https://openalex.org/W2370328482","https://openalex.org/W4287882779","https://openalex.org/W2046896701","https://openalex.org/W1996632063","https://openalex.org/W2140169421","https://openalex.org/W2265849288","https://openalex.org/W4378505325"],"abstract_inverted_index":{"A":[0],"double-loop":[1],"digraph":[2],"$G(N;s_1,s_2)=G(V,E)$":[3],"is":[4,131],"defined":[5],"by":[6],"$V={\\bf":[7],"Z}_N$":[8],"and":[9,33,121,148],"$E=\\{(i,i+s_1),":[10],"(i,i+s_2)|\\;":[11],"i\\in":[12],"V\\}$,":[13],"for":[14,64,80,124],"some":[15,146,149],"fixed":[16,66],"steps":[17],"$1\\leq":[18],"s_1":[19,39],"<":[20,22,40,42,45,47,71,73,95],"s_2":[21,41],"N$":[23],"with":[24,69,93],"$\\gcd(N,s_1,s_2)=1$.":[25],"Let":[26],"$D(N;s_1,s_2)$":[27],"be":[28],"the":[29,54,60,76,134,152],"diameter":[30,55],"of":[31,56,62,83,91,101,118,128,143],"$G$":[32],"let":[34],"us":[35],"define":[36],"$$":[37,49],"D(N)=\\min_{\\scriptstyle1\\leq":[38],"N,\\atop\\scriptstyle\\gcd(N,s_1,s_2)=1}D(N;s_1,s_2),\\quad":[43],"D_1(N)=\\min_{1":[44],"s":[46,72],"N}D(N;1,s).":[48],"Some":[50],"early":[51],"works":[52],"about":[53],"these":[57,144],"digraphs":[58],"studied":[59],"minimization":[61],"$D(N;1,s)$,":[63],"a":[65,116,122,141],"value":[67],"$N$,":[68,84],"$1":[70],"N$.":[74],"Although":[75],"identity":[77],"$D(N)=D_1(N)$":[78],"holds":[79],"infinite":[81,89,126],"values":[82,100],"there":[85],"are":[86,103,138,154],"also":[87],"another":[88],"set":[90],"integers":[92,107,120,130,137],"$D(N)":[94],"D_1(N)$.":[96],"These":[97],"other":[98],"integral":[99],"$N$":[102],"called":[104],"non-unit":[105],"step":[106],"or":[108],"nus":[109,119,129,136],"integers.":[110],"In":[111],"this":[112],"work":[113],"we":[114],"give":[115],"characterization":[117],"method":[123],"finding":[125],"families":[127],"developed.":[132],"Also":[133],"tight":[135],"classified.":[139],"As":[140],"consequence":[142],"results,":[145],"errata":[147],"flaws":[150],"in":[151],"bibliography":[153],"corrected.":[155]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}