Blikstad, J., Van Den Brand, J., Efron, Y. et al. (2 more authors) (2022) Nearly optimal communication and query complexity of bipartite matching. In: 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS). 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), 31 Oct - 03 Nov 2022, Denver, CO, USA. Institute of Electrical and Electronics Engineers (IEEE) , pp. 1174-1185. ISBN 9781665455206
Abstract
We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up to polylogarithmic factors in five models of computation: the two-party communication, AND query, OR query, XOR query, and quantum edge query models. Our results answer open problems that have been raised repeatedly since at least three decades ago [Hajnal, Maass, and Turan STOC’88; Ivanyos, Klauck, Lee, Santha, and de Wolf FSTTCS’12; Dobzinski, Nisan, and Oren STOC’14; Nisan SODA’21] and tighten the lower bounds shown by Beniamini and Nisan [STOC’21] and Zhang [ICALP’04]. We also settle the communication complexity of the generalizations of BMM, such as maximum-cost bipartite b-matching and transshipment; and the query complexity of unique bipartite perfect matching (answering an open question by Beniamini [2022]). Our algorithms and lower bounds follow from simple applications of known techniques such as cutting planes methods and set disjointness.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | F.1.1 Models of Computation; F.1.3 Complexity Measures and Classes; F.2 Analysis of Algorithms and Problem Complexity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 28 Jun 2023 12:26 |
Last Modified: | 28 Dec 2023 01:13 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/focs54457.2022.00113 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200970 |