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- W4313228059 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." @default.
- W4313228059 created "2023-01-06" @default.
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- W4313228059 date "2022-10-01" @default.
- W4313228059 modified "2023-10-07" @default.
- W4313228059 title "Nearly Optimal Communication and Query Complexity of Bipartite Matching" @default.
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- W4313228059 doi "https://doi.org/10.1109/focs54457.2022.00113" @default.
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