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- W2963324208 abstract "This paper gives drastically faster gossip algorithms to compute exact and approximate quantiles.Gossip algorithms, which allow each node to contact a uniformly random other node in each round, have been intensely studied and been adopted in many applications due to their fast convergence and their robustness to failures. Kempe et al. [24] gave gossip algorithms to compute important aggregate statistics if every node is given a value. In particular, they gave a beautiful O(logn + log 1 e ) round algorithm to e-approximate the sum of all values and an O(log2 n) round algorithm to compute the exact Φ-quantile, i.e., the ?Φn? smallest value.We give an quadratically faster and in fact optimal gossip algorithm for the exact Φ-quantile problem which runs in O(logn) rounds. We furthermore show that one can achieve an exponential speedup if one allows for an e-approximation. In particular, we give an O(log logn + log 1 e ) round gossip algorithm which computes a value of rank between Φn and (Φ + e)n at every node. Our algorithms are extremely simple and very robust - they can be operated with the same running times even if every transmission fails with a, potentially different, constant probability. We also give a matching Ω(log logn + log 1 e ) lower bound which shows that our algorithm is optimal for all values of e." @default.
- W2963324208 created "2019-07-30" @default.
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- W2963324208 date "2018-07-23" @default.
- W2963324208 modified "2023-10-16" @default.
- W2963324208 title "Optimal Gossip Algorithms for Exact and Approximate Quantile Computations" @default.
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- W2963324208 doi "https://doi.org/10.1145/3212734.3212770" @default.
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