arXiv 2010.024862020-10-06cs.DC

一般图中基于局部交易协议的单调分布负载均衡算法

Local Deal-Agreement Based Monotonic Distributed Algorithms for Load Balancing in General Graphs

Yefim Dinitz, Shlomi Dolev, Manish Kumar

备注：: 26 pages, 2 figures

摘要：

在计算机网络中，参与者可以在处理任务时进行合作，从而在它们之间平衡负载。我们提出了本地分布式算法，（反复）使用本地不平衡的标准，同时跨系统的参与者转移负载，迭代，直到所有负载平衡。我们的算法是基于一个简短的本地交易协议的建议/交易的通信，基于附近的负载。它们单调收敛，总是随着执行的进行提供更好的状态。此外，我们的算法避免了使负载暂时为负。因此，它们可以被认为是任何时间的，在这个意义上，它们可以在执行期间的任何时间停止。我们表明，我们的同步负载均衡算法实现$ε$ -平衡状态的连续设置和1-平衡状态的离散设置在所有的图形中，在$O(n D \log(n K/ε))$和$O(n D \log(n K/D) + n D^2)$时间，分别，其中$n$是节点数，$K$是初始差异，$D$是图形直径，和$ε$是最终的差异。我们的其他单调的同步和异步算法的离散设置的第一个算法，其中负载均衡是同时执行多个邻居的概括。这些算法到达一个1-平衡状态的时间$O(n K^2)$在一般的图形，但有可能更快的负载之间的所有邻居之间的平衡，而不是只有一个，我们描述了一个场景，演示了一个快速（$O(1)$）收敛的潜力。由于同步设置的限制，我们的异步算法避免了在进行下一个负载均衡步骤之前等待最慢的参与者的活动的需要。我们还介绍了我们的异步算法的自稳定版本。

英文摘要：

In computer networks, participants may cooperate in processing tasks, so that loads are balanced among them. We present local distributed algorithms that (repeatedly) use local imbalance criteria to transfer loads concurrently across the participants of the system, iterating until all loads are balanced. Our algorithms are based on a short local deal-agreement communication of proposal/deal, based on the neighborhood loads. They converge monotonically, always providing a better state as the execution progresses. Besides, our algorithms avoid making loads temporarily negative. Thus, they may be considered anytime ones, in the sense that they can be stopped at any time during the execution. We show that our synchronous load balancing algorithms achieve $ε$-Balanced state for the continuous setting and 1-Balanced state for the discrete setting in all graphs, within $O(n D \log(n K/ε))$ and $O(n D \log(n K/D) + n D^2)$ time, respectively, where $n$ is the number of nodes, $K$ is the initial discrepancy, $D$ is the graph diameter, and $ε$ is the final discrepancy. Our other monotonic synchronous and asynchronous algorithms for the discrete setting are generalizations of the first presented algorithms, where load balancing is performed concurrently with more than one neighbor. These algorithms arrive at a 1-Balanced state in time $O(n K^2)$ in general graphs, but have a potential to be faster as the loads are balanced among all neighbors, rather than with only one; we describe a scenario that demonstrates the potential for a fast ($O(1)$) convergence. Our asynchronous algorithm avoids the need to wait for the slowest participants' activity prior to making the next load balancing steps as synchronous settings restrict. We also introduce a self-stabilizing version of our asynchronous algorithm.

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摘要：

英文摘要：

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