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Shortest augmenting paths for online matchings on trees
online matchings
bipartite matchings
approximate matchings
shortest augmenting paths
dynamic graph algorithms
The shortest augmenting path (Sap) algorithm is one of the most classical approaches to the maximum matching and maximum flow problems, e.g., using it Edmonds and Karp (J. ACM 19(2), 248–264 1972) have shown the first strongly polynomial time algorithm for the maximum flow problem. Quite astonishingly, although it has been studied for many years already, this approach is far from being fully understood. This is exemplified by the online bipartite matching problem. In this problem a bipartite graph G = (W ⊎ B, E) is being revealed online, i.e., in each round one vertex from B with its incident edges arrives. After arrival of this vertex we augment the current matching by using shortest augmenting path. It was conjectured by Chaudhuri et al. (INFOCOM’09) that the total length of all augmenting paths found by Sap is O(nlogn). However, no better bound than O(n2) is known even for trees. In this paper we prove an O(nlog2n) upper bound for the total length of augmenting paths for trees.
cris.lastimport.wos | 2024-04-09T20:16:48Z | |
dc.abstract.en | The shortest augmenting path (Sap) algorithm is one of the most classical approaches to the maximum matching and maximum flow problems, e.g., using it Edmonds and Karp (J. ACM 19(2), 248–264 1972) have shown the first strongly polynomial time algorithm for the maximum flow problem. Quite astonishingly, although it has been studied for many years already, this approach is far from being fully understood. This is exemplified by the online bipartite matching problem. In this problem a bipartite graph G = (W ⊎ B, E) is being revealed online, i.e., in each round one vertex from B with its incident edges arrives. After arrival of this vertex we augment the current matching by using shortest augmenting path. It was conjectured by Chaudhuri et al. (INFOCOM’09) that the total length of all augmenting paths found by Sap is O(nlogn). However, no better bound than O(n2) is known even for trees. In this paper we prove an O(nlog2n) upper bound for the total length of augmenting paths for trees. | pl |
dc.affiliation | Wydział Matematyki i Informatyki : Zespół Katedr i Zakładów Informatyki Matematycznej | pl |
dc.contributor.author | Bosek, Bartłomiej - 114402 | pl |
dc.contributor.author | Leniowski, Dariusz | pl |
dc.contributor.author | Sankowski, Piotr | pl |
dc.contributor.author | Zych-Pawlewicz, Anna | pl |
dc.date.accessioned | 2018-03-09T10:00:41Z | |
dc.date.available | 2018-03-09T10:00:41Z | |
dc.date.issued | 2018 | pl |
dc.date.openaccess | 0 | |
dc.description.accesstime | w momencie opublikowania | |
dc.description.number | 2 | pl |
dc.description.physical | 337-348 | pl |
dc.description.version | ostateczna wersja wydawcy | |
dc.description.volume | 62 | pl |
dc.identifier.doi | 10.1007/s00224-017-9838-x | pl |
dc.identifier.eissn | 1433-0490 | pl |
dc.identifier.issn | 1432-4350 | pl |
dc.identifier.uri | https://ruj.uj.edu.pl/xmlui/handle/item/51539 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Udzielam licencji. Uznanie autorstwa 3.0 Polska | * |
dc.rights.licence | CC-BY | |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/pl/legalcode | * |
dc.share.type | inne | |
dc.subject.en | online matchings | pl |
dc.subject.en | bipartite matchings | pl |
dc.subject.en | approximate matchings | pl |
dc.subject.en | shortest augmenting paths | pl |
dc.subject.en | dynamic graph algorithms | pl |
dc.subtype | Article | pl |
dc.title | Shortest augmenting paths for online matchings on trees | pl |
dc.title.journal | Theory of Computing Systems | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |