Matches in SemOpenAlex for { <https://semopenalex.org/work/W2151348756> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W2151348756 endingPage "13" @default.
- W2151348756 startingPage "1" @default.
- W2151348756 abstract "In this article we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first nontrivial algorithm, with running time O ( mn ), dates back to König's work in 1916 (here m = nd is the number of edges in the graph, 2 n is the number of vertices, and d is the degree of each node). The currently most efficient algorithm takes time O(m) , and is due to Cole et al. [2001]. We improve this running time to O (min{ m , n 2.5 ln n / d }); this minimum can never be larger than O ( n 1.75 √ln n ). We obtain this improvement by proving a uniform sampling theorem: if we sample each edge in a d -regular bipartite graph independently with a probability p = O ( n ln n / d 2 ) then the resulting graph has a perfect matching with high probability. The proof involves a decomposition of the graph into pieces which are guaranteed to have many perfect matchings but do not have any small cuts. We then establish a correspondence between potential witnesses to nonexistence of a matching (after sampling) in any piece and cuts of comparable size in that same piece. Karger's sampling theorem [1994a, 1994b] for preserving cuts in a graph can now be adapted to prove our uniform sampling theorem for preserving perfect matchings. Using the O ( m √ n ) algorithm (due to Hopcroft and Karp [1973]) for finding maximum matchings in bipartite graphs on the sampled graph then yields the stated running time. We also provide an infinite family of instances to show that our uniform sampling result is tight up to polylogarithmic factors (in fact, up to ln 2 n )." @default.
- W2151348756 created "2016-06-24" @default.
- W2151348756 creator A5039619350 @default.
- W2151348756 creator A5051162653 @default.
- W2151348756 creator A5086773451 @default.
- W2151348756 date "2010-03-01" @default.
- W2151348756 modified "2023-10-16" @default.
- W2151348756 title "Perfect matchings via uniform sampling in regular bipartite graphs" @default.
- W2151348756 cites W1494735819 @default.
- W2151348756 cites W1971663478 @default.
- W2151348756 cites W2045107949 @default.
- W2151348756 cites W2053050060 @default.
- W2151348756 cites W2068888615 @default.
- W2151348756 cites W2120729889 @default.
- W2151348756 cites W2124624165 @default.
- W2151348756 cites W2125664420 @default.
- W2151348756 cites W2157529519 @default.
- W2151348756 cites W2170198451 @default.
- W2151348756 cites W4231916799 @default.
- W2151348756 doi "https://doi.org/10.1145/1721837.1721843" @default.
- W2151348756 hasPublicationYear "2010" @default.
- W2151348756 type Work @default.
- W2151348756 sameAs 2151348756 @default.
- W2151348756 citedByCount "8" @default.
- W2151348756 countsByYear W21513487562012 @default.
- W2151348756 countsByYear W21513487562013 @default.
- W2151348756 countsByYear W21513487562014 @default.
- W2151348756 countsByYear W21513487562017 @default.
- W2151348756 countsByYear W21513487562018 @default.
- W2151348756 countsByYear W21513487562019 @default.
- W2151348756 countsByYear W21513487562020 @default.
- W2151348756 crossrefType "journal-article" @default.
- W2151348756 hasAuthorship W2151348756A5039619350 @default.
- W2151348756 hasAuthorship W2151348756A5051162653 @default.
- W2151348756 hasAuthorship W2151348756A5086773451 @default.
- W2151348756 hasBestOaLocation W21513487562 @default.
- W2151348756 hasConcept C105795698 @default.
- W2151348756 hasConcept C114614502 @default.
- W2151348756 hasConcept C118615104 @default.
- W2151348756 hasConcept C132525143 @default.
- W2151348756 hasConcept C134119311 @default.
- W2151348756 hasConcept C149530733 @default.
- W2151348756 hasConcept C161487630 @default.
- W2151348756 hasConcept C165064840 @default.
- W2151348756 hasConcept C197657726 @default.
- W2151348756 hasConcept C203776342 @default.
- W2151348756 hasConcept C33923547 @default.
- W2151348756 hasConcept C36038622 @default.
- W2151348756 hasConcept C43517604 @default.
- W2151348756 hasConcept C51044901 @default.
- W2151348756 hasConceptScore W2151348756C105795698 @default.
- W2151348756 hasConceptScore W2151348756C114614502 @default.
- W2151348756 hasConceptScore W2151348756C118615104 @default.
- W2151348756 hasConceptScore W2151348756C132525143 @default.
- W2151348756 hasConceptScore W2151348756C134119311 @default.
- W2151348756 hasConceptScore W2151348756C149530733 @default.
- W2151348756 hasConceptScore W2151348756C161487630 @default.
- W2151348756 hasConceptScore W2151348756C165064840 @default.
- W2151348756 hasConceptScore W2151348756C197657726 @default.
- W2151348756 hasConceptScore W2151348756C203776342 @default.
- W2151348756 hasConceptScore W2151348756C33923547 @default.
- W2151348756 hasConceptScore W2151348756C36038622 @default.
- W2151348756 hasConceptScore W2151348756C43517604 @default.
- W2151348756 hasConceptScore W2151348756C51044901 @default.
- W2151348756 hasFunder F4320306076 @default.
- W2151348756 hasFunder F4320337387 @default.
- W2151348756 hasIssue "2" @default.
- W2151348756 hasLocation W21513487561 @default.
- W2151348756 hasLocation W21513487562 @default.
- W2151348756 hasLocation W21513487563 @default.
- W2151348756 hasOpenAccess W2151348756 @default.
- W2151348756 hasPrimaryLocation W21513487561 @default.
- W2151348756 hasRelatedWork W1515128446 @default.
- W2151348756 hasRelatedWork W1994363553 @default.
- W2151348756 hasRelatedWork W2091485261 @default.
- W2151348756 hasRelatedWork W2401632469 @default.
- W2151348756 hasRelatedWork W2509813159 @default.
- W2151348756 hasRelatedWork W2515819996 @default.
- W2151348756 hasRelatedWork W2609475100 @default.
- W2151348756 hasRelatedWork W3119766805 @default.
- W2151348756 hasRelatedWork W3206289552 @default.
- W2151348756 hasRelatedWork W4294024035 @default.
- W2151348756 hasVolume "6" @default.
- W2151348756 isParatext "false" @default.
- W2151348756 isRetracted "false" @default.
- W2151348756 magId "2151348756" @default.
- W2151348756 workType "article" @default.