Approximate shared-memory counting despite a strong adversary
Approximate shared-memory counting despite a strong adversary
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尽管对手强大，但仍近似共享内存计数
DOI：
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发表时间：
2009
期刊：
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通讯作者：
K. Censor
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文献类型：
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作者：
J. Aspnes;K. Censor
给出了一个新的随机异步共享内存数据结构，用于实现一个近似计数器，该计数器可以通过模型中的每个<i> n </i>进程来递增一次，该过程允许最多允许<i> n> n> -1碰撞失败。 <sup> <i> o </i>（1/＆epsis;）</sup>）登记操作， <i> o </i>（<i> n </i> <sup> 4/5+＆epsis; </sup>（（（1/δ）log <i> n </i>）<sup> < i> o </i>（1/＆epsis;）</sup>）每个读取量。均值的流程和工作目的地的数量，可以观察过程内部状态的强大广告调度程序。
改进的计数器的应用是一种改进的协议，用于求解随机共享内存共识，从而从<i> o </i>（<i> n> n log <i> N </i>）到最佳<i> o </i>（<i> n </i>），解决了有关此模型中关于共识的最后一个剩下的开放问题之一。
A new randomized asynchronous shared-memory data structure is given for implementing an approximate counter that can be incremented once by each of <i>n</i> processes in a model that allows up to <i>n</i>−1 crash failures. For any fixed &epsis;, the counter achieves a relative error of Δ with high probability, at the cost of <i>O</i>(((1/Δ) log <i>n</i>)<sup><i>O</i>(1/&epsis;)</sup>) register operations per increment and <i>O</i>(<i>n</i><sup>4/5+&epsis;</sup>((1/Δ) log <i>n</i>)<sup><i>O</i>(1/&epsis;)</sup>) register operations per read. The counter combines randomized sampling for estimating large values with an expander for estimating small values. This is the first counter implementation that is sublinear the number of processes and works despite a strong adversary scheduler that can observe internal states of processes.
An application of the improved counter is an improved protocol for solving randomized shared-memory consensus, which reduces the best previously known individual work complexity from <i>O</i>(<i>n</i> log <i>n</i>) to an optimal <i>O</i>(<i>n</i>), resolving one of the last remaining open problems concerning consensus in this model.