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- W4384808009 abstract "In this paper, we give new auction algorithms for maximum weighted bipartite matching (MWM) and maximum cardinality bipartite $b$-matching (MCbM). Our algorithms run in $Oleft(log n/varepsilon^8right)$ and $Oleft(log n/varepsilon^2right)$ rounds, respectively, in the blackboard distributed setting. We show that our MWM algorithm can be implemented in the distributed, interactive setting using $O(log^2 n)$ and $O(log n)$ bit messages, respectively, directly answering the open question posed by Demange, Gale and Sotomayor [DNO14]. Furthermore, we implement our algorithms in a variety of other models including the the semi-streaming model, the shared-memory work-depth model, and the massively parallel computation model. Our semi-streaming MWM algorithm uses $O(1/varepsilon^8)$ passes in $O(n log n cdot log(1/varepsilon))$ space and our MCbM algorithm runs in $O(1/varepsilon^2)$ passes using $Oleft(left(sum_{i in L} b_i + |R|right)log(1/varepsilon)right)$ space (where parameters $b_i$ represent the degree constraints on the $b$-matching and $L$ and $R$ represent the left and right side of the bipartite graph, respectively). Both of these algorithms improves emph{exponentially} the dependence on $varepsilon$ in the space complexity in the semi-streaming model against the best-known algorithms for these problems, in addition to improvements in round complexity for MCbM. Finally, our algorithms eliminate the large polylogarithmic dependence on $n$ in depth and number of rounds in the work-depth and massively parallel computation models, respectively, improving on previous results which have large polylogarithmic dependence on $n$ (and exponential dependence on $varepsilon$ in the MPC model)." @default.
- W4384808009 created "2023-07-20" @default.
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- W4384808009 date "2023-07-18" @default.
- W4384808009 modified "2023-09-26" @default.
- W4384808009 title "Scalable Auction Algorithms for Bipartite Maximum Matching Problems" @default.
- W4384808009 doi "https://doi.org/10.48550/arxiv.2307.08979" @default.
- W4384808009 hasPublicationYear "2023" @default.
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