# Online Bipartite Matching with Decomposable Weights

## Author(s): Charikar, Moses; Henzinger, Monika; Nguyễn, Huy L

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1rj93
DC FieldValueLanguage
dc.contributor.authorCharikar, Moses-
dc.contributor.authorHenzinger, Monika-
dc.contributor.authorNguyễn, Huy L-
dc.date.accessioned2021-10-08T19:44:40Z-
dc.date.available2021-10-08T19:44:40Z-
dc.date.issued2014en_US
dc.identifier.citationCharikar, Moses, Monika Henzinger, and Huy L. Nguyễn. "Online Bipartite Matching with Decomposable Weights." Algorithms - ESA (2014): 260-271. doi: 10.1007/978-3-662-44777-2_22en_US
dc.identifier.issn0302-9743-
dc.identifier.urihttps://arxiv.org/pdf/1409.2139.pdf-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1rj93-
dc.description.abstractWe study a weighted online bipartite matching problem: G(V 1, V 2, E) is a weighted bipartite graph where V 1 is known beforehand and the vertices of V 2 arrive online. The goal is to match vertices of V 2 as they arrive to vertices in V 1, so as to maximize the sum of weights of edges in the matching. If assignments to V 1 cannot be changed, no bounded competitive ratio is achievable. We study the weighted online matching problem with free disposal, where vertices in V 1 can be assigned multiple times, but only get credit for the maximum weight edge assigned to them over the course of the algorithm. For this problem, the greedy algorithm is 0.5-competitive and determining whether a better competitive ratio is achievable is a well known open problem. We identify an interesting special case where the edge weights are decomposable as the product of two factors, one corresponding to each end point of the edge. This is analogous to the well studied related machines model in the scheduling literature, although the objective functions are different. For this case of decomposable edge weights, we design a 0.5664 competitive randomized algorithm in complete bipartite graphs. We show that such instances with decomposable weights are non-trivial by establishing upper bounds of 0.618 for deterministic and 0.8 for randomized algorithms. A tight competitive ratio of 1 − 1/e ≈ 0.632 was known previously for both the 0-1 case as well as the case where edge weights depend on the offline vertices only, but for these cases, reassignments cannot change the quality of the solution. Beating 0.5 for weighted matching where reassignments are necessary has been a significant challenge. We thus give the first online algorithm with competitive ratio strictly better than 0.5 for a non-trivial case of weighted matching with free disposal.en_US
dc.format.extent260 - 271en_US
dc.language.isoen_USen_US
dc.relation.ispartofAlgorithms - ESAen_US
dc.relation.ispartofseriesLecture Notes in Computer Science;-
dc.rightsAuthor's manuscripten_US
dc.titleOnline Bipartite Matching with Decomposable Weightsen_US
dc.typeConference Articleen_US
dc.identifier.doi10.1007/978-3-662-44777-2_22-
dc.identifier.eissn1611-3349-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceedingen_US

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