{"id":"https://openalex.org/W148606920","doi":"https://doi.org/10.1023/a:1026198523981","title":"On Center Cycles in Grid Graphs","display_name":"On Center Cycles in Grid Graphs","publication_year":2003,"publication_date":"2003-09-01","ids":{"openalex":"https://openalex.org/W148606920","doi":"https://doi.org/10.1023/a:1026198523981","mag":"148606920"},"language":"en","primary_location":{"id":"doi:10.1023/a:1026198523981","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1026198523981","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/4690","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003787332","display_name":"L. R. Foulds","orcid":"https://orcid.org/0000-0001-7538-8263"},"institutions":[{"id":"https://openalex.org/I52179390","display_name":"University of Waikato","ror":"https://ror.org/013fsnh78","country_code":"NZ","type":"education","lineage":["https://openalex.org/I52179390"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Les R. Foulds","raw_affiliation_strings":["Department of Management Systems, University of Waikato, Private Bag 3105, Hamilton, 2020, New Zealand","Department of Management Systems University of Waikato Hamilton New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Systems, University of Waikato, Private Bag 3105, Hamilton, 2020, New Zealand","institution_ids":["https://openalex.org/I52179390"]},{"raw_affiliation_string":"Department of Management Systems University of Waikato Hamilton New Zealand","institution_ids":["https://openalex.org/I52179390"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111683448","display_name":"Horst W. Hamacher","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Horst W. Hamacher","raw_affiliation_strings":["Fachbereich Mathematik, Universit\u00e4t Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","Fachbereich Mathematik , Universit\u00e4t Kaiserslautern , Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00e4t Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Fachbereich Mathematik , Universit\u00e4t Kaiserslautern , Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073713999","display_name":"Anita Sch\u00f6bel","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anita Sch\u00f6bel","raw_affiliation_strings":["Fachbereich Mathematik, Universit\u00e4t Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","Fachbereich Mathematik , Universit\u00e4t Kaiserslautern , Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00e4t Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Fachbereich Mathematik , Universit\u00e4t Kaiserslautern , Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044970442","display_name":"Tadashi Yamaguchi","orcid":"https://orcid.org/0000-0001-5761-4888"},"institutions":[{"id":"https://openalex.org/I159165171","display_name":"Hokkaido Information University","ror":"https://ror.org/00nyxpe17","country_code":"JP","type":"education","lineage":["https://openalex.org/I159165171"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tadashi Yamaguchi","raw_affiliation_strings":["Faculty of Information Media, Hokkaido Information University, Nishinopporo 59-2, Hokkaido, 069-8585, Japan","Faculty of Information Media, Hokkaido Information University, Hokkaido, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Media, Hokkaido Information University, Nishinopporo 59-2, Hokkaido, 069-8585, Japan","institution_ids":["https://openalex.org/I159165171"]},{"raw_affiliation_string":"Faculty of Information Media, Hokkaido Information University, Hokkaido, Japan","institution_ids":["https://openalex.org/I159165171"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7759,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.73089725,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"122","issue":"1-4","first_page":"163","last_page":"175"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.30250000953674316,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.30250000953674316,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.2946000099182129,"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/T14270","display_name":"Simulation and Modeling Applications","score":0.2671999931335449,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/cardinality","display_name":"Cardinality (data modeling)","score":0.7312122583389282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7091666460037231},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.6623677015304565},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6594366431236267},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5196903347969055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5004987716674805},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4983980655670166},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4548746347427368},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.41555094718933105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16704010963439941},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14961856603622437}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7312122583389282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7091666460037231},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.6623677015304565},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6594366431236267},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5196903347969055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5004987716674805},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4983980655670166},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4548746347427368},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.41555094718933105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16704010963439941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14961856603622437},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1023/a:1026198523981","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1026198523981","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:annopr:v:122:y:2003:i:1:p:163-175:10.1023/a:1026198523981","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1023/A:1026198523981","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/4690","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/4690","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:publications.goettingen-research-online.de:2/4690","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/4690","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W159151393","https://openalex.org/W606008011","https://openalex.org/W637475318","https://openalex.org/W768332614","https://openalex.org/W1555798585","https://openalex.org/W1591736593","https://openalex.org/W1966054643","https://openalex.org/W1972062617","https://openalex.org/W1975600022","https://openalex.org/W2011039300","https://openalex.org/W2023972910","https://openalex.org/W2035792515","https://openalex.org/W2038947920","https://openalex.org/W2039293736","https://openalex.org/W2040896439","https://openalex.org/W2074897537","https://openalex.org/W2109396997","https://openalex.org/W2110824994","https://openalex.org/W2133241632","https://openalex.org/W2134531991","https://openalex.org/W2475595550","https://openalex.org/W4285719527","https://openalex.org/W6618415984","https://openalex.org/W6635579006","https://openalex.org/W6660001639","https://openalex.org/W6687414330"],"related_works":["https://openalex.org/W2242098268","https://openalex.org/W4244945894","https://openalex.org/W2760515006","https://openalex.org/W2802042052","https://openalex.org/W1987609185","https://openalex.org/W2003462717","https://openalex.org/W4224881918","https://openalex.org/W174828583","https://openalex.org/W2485961789","https://openalex.org/W2063135098"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2016-06-24T00:00:00"}
