{"id":"https://openalex.org/W3151200418","doi":"https://doi.org/10.1137/16m1106225","title":"Algorithms for Weighted Matching Generalizations II: <i>f</i>-factors and the Special Case of Shortest Paths","display_name":"Algorithms for Weighted Matching Generalizations II: <i>f</i>-factors and the Special Case of Shortest Paths","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3151200418","doi":"https://doi.org/10.1137/16m1106225","mag":"3151200418"},"language":"en","primary_location":{"id":"doi:10.1137/16m1106225","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1106225","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106225","source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106225","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001013961","display_name":"Harold N. Gabow","orcid":"https://orcid.org/0000-0002-9775-3492"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Harold N. Gabow","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025494465","display_name":"Piotr Sankowski","orcid":"https://orcid.org/0000-0002-0907-3754"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piotr Sankowski","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001013961"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07315069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"2","first_page":"555","last_page":"601"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":1.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":1.0,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T12288","display_name":"Optimization and Search Problems","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7923097610473633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7789291143417358},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4970443546772003},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.49692848324775696},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4805762767791748},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.47435009479522705},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44399237632751465},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.414799302816391},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.41224706172943115},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3647214472293854}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7923097610473633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7789291143417358},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4970443546772003},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.49692848324775696},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4805762767791748},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.47435009479522705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44399237632751465},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.414799302816391},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.41224706172943115},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3647214472293854},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1106225","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1106225","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106225","source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/16m1106225","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1106225","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106225","source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2464966296","display_name":null,"funder_award_id":"772346","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3151200418.pdf","grobid_xml":"https://content.openalex.org/works/W3151200418.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1509653541","https://openalex.org/W1970824097","https://openalex.org/W2004116976","https://openalex.org/W2008034501","https://openalex.org/W2008816808","https://openalex.org/W2010255818","https://openalex.org/W2028503265","https://openalex.org/W2066470474","https://openalex.org/W2090168101","https://openalex.org/W2091299439","https://openalex.org/W2094090625","https://openalex.org/W2125690626","https://openalex.org/W2136442765","https://openalex.org/W2136481365","https://openalex.org/W2227557434","https://openalex.org/W2327315803","https://openalex.org/W2551688242","https://openalex.org/W2782000683","https://openalex.org/W2950975603","https://openalex.org/W3163104596"],"related_works":["https://openalex.org/W3127082728","https://openalex.org/W2067936666","https://openalex.org/W2036758175","https://openalex.org/W3046990805","https://openalex.org/W4287691960","https://openalex.org/W3097369619","https://openalex.org/W1994598067","https://openalex.org/W2061496873","https://openalex.org/W2011106535","https://openalex.org/W2963622642"],"abstract_inverted_index":{"For":[0,22,60,70],"an":[1,12,135],"undirected":[2,104],"graph":[3],"or":[4,132,148],"multigraph":[5],"$G=(V,E)$":[6],"and":[7,44,56],"a":[8,15,33,83,97,112,122],"function":[9,19],"$f:V\\to":[10],"\\mathbb{Z_+}$,":[11],"$f$-factor":[13,36],"is":[14,20,46,54,65,75,80],"subgraph":[16],"whose":[17],"degree":[18],"$f$.":[21],"integral":[23],"edge":[24],"weights":[25],"of":[26,49,86,89,114],"maximum":[27,34,138],"magnitude":[28],"$W$":[29],"our":[30],"algorithm":[31,53,64,74,79,124,136],"finds":[32],"weight":[35,139],"in":[37,102],"time":[38,62,72,128,142],"$\\tilde{O}(Wf(V)^{\\omega})$,":[39],"where":[40],"$f(V)=\\sum_{v\\in":[41],"V}":[42],"f(v)$":[43],"$\\omega$":[45],"the":[47,63,73,87,90,107,126],"exponent":[48],"matrix":[50],"multiplication.":[51],"The":[52,78,116],"randomized":[55,123],"has":[57],"two":[58],"versions.":[59],"worst-case":[61],"correct":[66],"with":[67,125],"high":[68],"probability.":[69],"expected":[71],"Las":[76],"Vegas.":[77],"based":[81],"on":[82],"detailed":[84],"analysis":[85],"structure":[88],"optimum":[91],"blossoms.":[92],"A":[93],"special":[94],"case":[95],"gives":[96],"representation":[98,117],"for":[99,137],"single-source":[100],"shortest-paths":[101],"conservative":[103],"graphs,":[105],"generalizing":[106],"standard":[108],"shortest-path":[109],"tree":[110],"to":[111],"\u201ctree":[113],"cycles\u201d.":[115],"can":[118],"be":[119],"constructed":[120],"by":[121,134],"same":[127],"bound":[129],"as":[130],"above,":[131],"deterministically":[133],"matching,":[140],"achieving":[141],"$O(n(m":[143],"+":[144],"n":[145],"\\log":[146,152],"n))$":[147],"$O(\\sqrt{n":[149],"}\\":[150],"m":[151],"(nW))$.":[153]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
