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- W2770292951 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. [FOCS'03] gave gossip algorithms to compute important aggregate statistics if every node is given a value. In particular, they gave a beautiful $O(log n + log frac{1}{epsilon})$ round algorithm to $epsilon$-approximate the sum of all values and an $O(log^2 n)$ round algorithm to compute the exact $phi$-quantile, i.e., the the $lceil phi n rceil$ smallest value. We give an quadratically faster and in fact optimal gossip algorithm for the exact $phi$-quantile problem which runs in $O(log n)$ rounds. We furthermore show that one can achieve an exponential speedup if one allows for an $epsilon$-approximation. We give an $O(log log n + log frac{1}{epsilon})$ round gossip algorithm which computes a value of rank between $phi n$ and $(phi+epsilon)n$ at every node.% for any $0 leq phi leq 1$ and $0 < epsilon < 1$. 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 $Omega(log log n + log frac{1}{epsilon})$ lower bound which shows that our algorithm is optimal for all values of $epsilon$." @default.
- W2770292951 created "2017-12-04" @default.
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- W2770292951 date "2017-11-25" @default.
- W2770292951 modified "2023-10-16" @default.
- W2770292951 title "Optimal Gossip Algorithms for Exact and Approximate Quantile Computations" @default.
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- W2770292951 doi "https://doi.org/10.48550/arxiv.1711.09258" @default.
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