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arXiv cs/0611098cs.DCcs.DS
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一种有效的分布式互斥算法分析(路径互斥的平均-实例分析)

Analysis of an Efficient Distributed Algorithm for Mutual Exclusion (Average-Case Analysis of Path Reversal)

Christian Lavault

摘要:

Naïmi、Trehe和Arnold分析的算法是第一个解决完全网络中互斥问题的分布式算法,它使用动态逻辑树结构作为其基本分布式数据结构,即根节点树中的路径反转变换;此外,它也是第一个实现对数平均情况消息复杂度的算法。本文提出了一种计算路径反转代价矩的直接而通用的方法。它基本上使用组合结构和相关的概率生成函数之间的一一对应关系:路径反转的期望成本因此被证明是精确的$H_{n-1}$。此外,还给出了算法的时间复杂度和消息复杂度,以及算法在任意网络中最坏情况消息复杂度的随机界。完成了路径反转的平均情况分析和分布式互斥算法的分析。所使用的一般技术也应该证明是可用的和富有成效的,当适应最有效的最近的基于树的分布式算法互斥需要强大的工具,特别是平均情况下的分析。

英文摘要:

The algorithm analysed by Naïmi, Trehe and Arnold was the very first distributed algorithm to solve the mutual exclusion problem in complete networks by using a dynamic logical tree structure as its basic distributed data structure, viz. a path reversal transformation in rooted n-node trees; besides, it was also the first one to achieve a logarithmic average-case message complexity. The present paper proposes a direct and general approach to compute the moments of the cost of path reversal. It basically uses one-one correspondences between combinatorial structures and the associated probability generating functions: the expected cost of path reversal is thus proved to be exactly $H_{n-1}$. Moreover, time and message complexity of the algorithm as well as randomized bounds on its worst-case message complexity in arbitrary networks are also given. The average-case analysis of path reversal and the analysis of this distributed algorithm for mutual exclusion are thus fully completed in the paper. The general techniques used should also prove available and fruitful when adapted to the most efficient recent tree-based distributed algorithms for mutual exclusion which require powerful tools, particularly for average-case analyses.

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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