{"id":"https://openalex.org/W1561275246","doi":"https://doi.org/10.1007/11618058_1","title":"Crossings and Permutations","display_name":"Crossings and Permutations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1561275246","doi":"https://doi.org/10.1007/11618058_1","mag":"1561275246"},"language":"en","primary_location":{"id":"doi:10.1007/11618058_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11618058_1","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5038712987","display_name":"Th\u00e9r\u00e8se Biedl","orcid":"https://orcid.org/0000-0002-9003-3783"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Therese Biedl","raw_affiliation_strings":["School of Computer Science, University of Waterloo, ON, N2L3G1, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, ON, N2L3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080729232","display_name":"Franz J. Brandenburg","orcid":"https://orcid.org/0000-0001-6544-8496"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Franz J. Brandenburg","raw_affiliation_strings":["Lehrstuhl f\u00fcr Informatik, Universit\u00e4t Passau, 94030, Passau, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Informatik, Universit\u00e4t Passau, 94030, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100638710","display_name":"Xiaotie Deng","orcid":"https://orcid.org/0000-0002-5282-6467"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiaotie Deng","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, SAR, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, SAR, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038712987"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.0919,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.85556003,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9883000254631042,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9883000254631042,"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/T11106","display_name":"Data Management and Algorithms","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9789999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.756345272064209},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.740617036819458},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7201734185218811},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6861825585365295},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.6804360151290894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6138637661933899},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4886920750141144},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4501743018627167},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4291653633117676},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4224369525909424},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4116029739379883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2543727457523346},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1525786817073822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06674927473068237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06605130434036255}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.756345272064209},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.740617036819458},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7201734185218811},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6861825585365295},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.6804360151290894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6138637661933899},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4886920750141144},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4501743018627167},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4291653633117676},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4224369525909424},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4116029739379883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2543727457523346},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1525786817073822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06674927473068237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06605130434036255},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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":2,"locations":[{"id":"doi:10.1007/11618058_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11618058_1","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:gdea.informatik.uni-koeln.de:675","is_oa":false,"landing_page_url":"http://gdea.informatik.uni-koeln.de/675/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196197","display_name":"gdea - Graph Drawing E-print Archive (GDEA)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W356477583","https://openalex.org/W1504064237","https://openalex.org/W1505320659","https://openalex.org/W1519350920","https://openalex.org/W1600537614","https://openalex.org/W1685029458","https://openalex.org/W1931404780","https://openalex.org/W1965752728","https://openalex.org/W1972151695","https://openalex.org/W2011039300","https://openalex.org/W2011218826","https://openalex.org/W2013372570","https://openalex.org/W2032884539","https://openalex.org/W2051834357","https://openalex.org/W2060538865","https://openalex.org/W2070745908","https://openalex.org/W2071353749","https://openalex.org/W2079962198","https://openalex.org/W2089788538","https://openalex.org/W2099281231","https://openalex.org/W2102664288","https://openalex.org/W2167372977","https://openalex.org/W2318031348","https://openalex.org/W6640487201"],"related_works":["https://openalex.org/W1962528574","https://openalex.org/W2949296767","https://openalex.org/W4291556630","https://openalex.org/W3215419002","https://openalex.org/W1561275246","https://openalex.org/W2158949528","https://openalex.org/W2563949111","https://openalex.org/W2369914007","https://openalex.org/W2195803831","https://openalex.org/W1643959696"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
