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- W4380874235 abstract "The maximum weighted matching (mwm) problem is one of the most well-studied combinatorial optimization problems in distributed graph algorithms. Despite a long development on the problem, and the recent progress of Fischer, Mitrovic, and Uitto [16] who gave a poly(1/ϵ, log n)-round algorithm for obtaining a (1 − ϵ)-approximate solution for unweighted maximum matching, it had been an open problem whether a (1 − ϵ)-approximate mwm can be obtained in poly(1/ϵ, log n) rounds in the CONGEST model. Algorithms with such running times were only known for special graph classes such as bipartite graphs [1] and minor-free graphs [8]. For general graphs, the previously known algorithms require exponential in (1/ϵ) rounds for obtaining a (1 − ϵ)-approximate solution [13] or achieve an approximation factor of at most 2/3 [1]. In this work, we settle this open problem by giving a deterministic poly(1/ϵ, log n)-round algorithm for computing a (1 − ϵ)-approximate mwm for general graphs in the CONGEST model. Our proposed solution extends the algorithm of Fischer, Mitrovic, and Uitto [16], blends in the sequential algorithm from Duan and Pettie [11] and the work of Faour, Fuchs, and Kuhn [13]. Interestingly, this solution also implies a CREW PRAM algorithm with poly(1/ϵ, log n) span using only O(m) processors, and a poly(1/ϵ)-passes algorithm in the semi-streaming model." @default.
- W4380874235 created "2023-06-17" @default.
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- W4380874235 date "2023-06-16" @default.
- W4380874235 modified "2023-10-16" @default.
- W4380874235 title "(1- <i>ϵ</i> )-Approximate Maximum Weighted Matching in poly(1/ <i>ϵ</i> , log <i>n</i> ) Time in the Distributed and Parallel Settings" @default.
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- W4380874235 doi "https://doi.org/10.1145/3583668.3594570" @default.
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