计算可分离函数的快速分布式算法
Fast Distributed Algorithms for Computing Separable Functions
摘要：
以完全分布式的方式计算网络中节点处的值的函数的问题，其中节点不具有唯一的身份并且仅基于本地信息做出决策，在传感器、对等网络和ad-hoc网络中具有应用。在这方面的任务，计算可分离的功能，它可以被写为线性组合的功能，个别变量，研究。用于求平均的已知迭代算法可以用于计算这样的函数的归一化值，但是这些算法一般不扩展到可分离函数的实际值的计算。本文的主要贡献是设计了一个计算可分函数的分布式随机算法。算法的运行时间取决于作为子程序使用的最小计算算法的运行时间。使用一个随机八卦机制的最小计算作为子程序产生一个完整的完全分布式算法计算可分离的功能。对于一类具有小的谱间隙的图，例如网格图，由该算法计算平均值所使用的时间比已知的迭代平均方案所需的时间小。
英文摘要：
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and ad-hoc networks. The task of computing separable functions, which can be written as linear combinations of functions of individual variables, is studied in this context. Known iterative algorithms for averaging can be used to compute the normalized values of such functions, but these algorithms do not extend in general to the computation of the actual values of separable functions. The main contribution of this paper is the design of a distributed randomized algorithm for computing separable functions. The running time of the algorithm is shown to depend on the running time of a minimum computation algorithm used as a subroutine. Using a randomized gossip mechanism for minimum computation as the subroutine yields a complete totally distributed algorithm for computing separable functions. For a class of graphs with small spectral gap, such as grid graphs, the time used by the algorithm to compute averages is of a smaller order than the time required by a known iterative averaging scheme.
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