arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1706.03992cs.DC
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循环的分布式检测

Distributed Detection of Cycles

Pierre Fraigniaud, Dennis Olivetti

摘要:

Brakerski和Patt-Shamir(2011)引入了网络中的分布式属性测试,其目的是以分布式方式检测大型密集子网络的存在。最近,Censor-Hillel等人(2016)已经展示了如何通过分布式算法在恒定数量的轮次中检测3-循环。在后续工作中,Fraigniaud等人(2016)也展示了如何在恒定数量的轮中检测4个周期。然而,这些后面的工作中的技术被证明不能推广到更大的周期$C_k$与$k\geq 5$。在本文中,我们完全解决了循环检测的问题,通过建立以下结果。对于每一个$k\geq 3$,存在一个分布式的属性测试算法的$C_k$ -freeness,在一个恒定的回合数。所有这些结果都适用于经典的分布式网络计算CONGEST模型。我们的算法是单侧误差。它的轮复杂度是$O(1/ε)$,其中$ε\in(0,1)$是测量合法和非法实例之间的差距的属性测试参数。

英文摘要:

Distributed property testing in networks has been introduced by Brakerski and Patt-Shamir (2011), with the objective of detecting the presence of large dense sub-networks in a distributed manner. Recently, Censor-Hillel et al. (2016) have shown how to detect 3-cycles in a constant number of rounds by a distributed algorithm. In a follow up work, Fraigniaud et al. (2016) have shown how to detect 4-cycles in a constant number of rounds as well. However, the techniques in these latter works were shown not to generalize to larger cycles $C_k$ with $k\geq 5$. In this paper, we completely settle the problem of cycle detection, by establishing the following result. For every $k\geq 3$, there exists a distributed property testing algorithm for $C_k$-freeness, performing in a constant number of rounds. All these results hold in the classical CONGEST model for distributed network computing. Our algorithm is 1-sided error. Its round-complexity is $O(1/ε)$ where $ε\in(0,1)$ is the property testing parameter measuring the gap between legal and illegal instances.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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