Nearly Optimal Communication and Query Complexity of Bipartite Matching

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 repea...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 1174 - 1185
Main Authors: Blikstad, Joakim, Van Den Brand, Jan, Efron, Yuval, Mukhopadhyay, Sagnik, Nanongkai, Danupon
Format: Conference Proceeding
Language:English
Published: IEEE 01.10.2022
Subjects:
Analytical models
Complexity theory
Computational modeling
Computer science
F.1.1 Models of Computation
F.1.3 Complexity Measures and Classes
F.2 Analysis of Algorithms and Problem Complexity
Quantum computing
ISSN:2575-8454
Online Access:Get full text
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Summary: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.
ISSN:2575-8454
DOI:10.1109/FOCS54457.2022.00113