{"id":"https://openalex.org/W2103086309","doi":"https://doi.org/10.1017/s0963548306008157","title":"Completing a (<i>k</i> \u2212 1)-Assignment","display_name":"Completing a (<i>k</i> \u2212 1)-Assignment","publication_year":2007,"publication_date":"2007-02-21","ids":{"openalex":"https://openalex.org/W2103086309","doi":"https://doi.org/10.1017/s0963548306008157","mag":"2103086309"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548306008157","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306008157","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5031800301","display_name":"Svante Linusson","orcid":"https://orcid.org/0000-0001-6339-2230"},"institutions":[{"id":"https://openalex.org/I4210103991","display_name":"Swedish e-Science Research Centre","ror":"https://ror.org/01e59yk92","country_code":"SE","type":"facility","lineage":["https://openalex.org/I4210103991"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"SVANTE LINUSSON","raw_affiliation_strings":["Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden (e-mail:","Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden (e-mail: linusson@math.kth.se)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden (e-mail:","institution_ids":["https://openalex.org/I86987016","https://openalex.org/I4210103991"]},{"raw_affiliation_string":"Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden (e-mail: linusson@math.kth.se)#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087020456","display_name":"Johan W\u00e4stlund","orcid":null},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"JOHAN W\u00c4STLUND","raw_affiliation_strings":["Department of Mathematics, Link\u00f6ping University, 581 83 Link\u00f6ping, Sweden (e-mail:","Department of Mathematics, Link\u00f6ping University, 581 83 Link\u00f6ping, Sweden (e-mail: jowas@mai.liu.se)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Link\u00f6ping University, 581 83 Link\u00f6ping, Sweden (e-mail:","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Department of Mathematics, Link\u00f6ping University, 581 83 Link\u00f6ping, Sweden (e-mail: jowas@mai.liu.se)#TAB#","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.16039886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"4","first_page":"621","last_page":"629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9950000047683716,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/random-variable","display_name":"Random variable","score":0.7098583579063416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6509206891059875},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6395667791366577},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.59837406873703},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5547479391098022},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.5486378073692322},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.5227706432342529},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5224722623825073},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5103644728660583},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4935978651046753},{"id":"https://openalex.org/keywords/random-assignment","display_name":"Random assignment","score":0.4922560751438141},{"id":"https://openalex.org/keywords/laplace-distribution","display_name":"Laplace distribution","score":0.4579668343067169},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4328976273536682},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.417741596698761},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3222062289714813},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3221658170223236},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2832207679748535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18766477704048157}],"concepts":[{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.7098583579063416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6509206891059875},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6395667791366577},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.59837406873703},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5547479391098022},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.5486378073692322},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.5227706432342529},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5224722623825073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5103644728660583},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4935978651046753},{"id":"https://openalex.org/C129410224","wikidata":"https://www.wikidata.org/wiki/Q7291958","display_name":"Random assignment","level":2,"score":0.4922560751438141},{"id":"https://openalex.org/C183057437","wikidata":"https://www.wikidata.org/wiki/Q671617","display_name":"Laplace distribution","level":3,"score":0.4579668343067169},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4328976273536682},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.417741596698761},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3222062289714813},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3221658170223236},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2832207679748535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18766477704048157},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548306008157","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306008157","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.238.300","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.238.300","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0410347v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.447.9717","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.447.9717","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.chalmers.se/~wastlund/Completingk-1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1504317671","https://openalex.org/W1608109024","https://openalex.org/W1643558380","https://openalex.org/W1930604537","https://openalex.org/W1980848544","https://openalex.org/W2028955990","https://openalex.org/W2054516710","https://openalex.org/W2070993566","https://openalex.org/W2099870086","https://openalex.org/W2119414881","https://openalex.org/W2153359656","https://openalex.org/W2161369484","https://openalex.org/W2529617700","https://openalex.org/W2914659449","https://openalex.org/W4247422315","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W2094164772","https://openalex.org/W2013281523","https://openalex.org/W1992254807","https://openalex.org/W2068546026","https://openalex.org/W2046036316","https://openalex.org/W3039003513","https://openalex.org/W2340267985","https://openalex.org/W1984505799","https://openalex.org/W2485229344","https://openalex.org/W2517500088"],"abstract_inverted_index":{"We":[0,29],"consider":[1],"the":[2,5,8,19,35,48],"distribution":[3],"of":[4,7,38],"value":[6,46],"optimal":[9],"k":[10,56],"-assignment":[11],"in":[12],"an":[13],"m":[14],"\u00d7":[15],"n":[16],"matrix,":[17],"where":[18],"entries":[20],"are":[21],"independent":[22],"exponential":[23],"random":[24,40],"variables":[25],"with":[26],"arbitrary":[27],"rates.":[28],"give":[30],"closed":[31],"formulas":[32],"for":[33,43],"both":[34],"Laplace":[36],"transform":[37],"this":[39],"variable":[41],"and":[42],"its":[44],"expected":[45],"under":[47],"condition":[49],"that":[50],"there":[51],"is":[52],"a":[53],"zero-cost":[54],"(":[55],"\u2212":[57],"1)-assignment.":[58]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}