We presented a snap-stabilizing m-wave algorithm implementing waves originating from multiple initiators for a tree network. The proposed algorithm guarantees that even the first m-wave started by initiators succeeds in delivering a message to each process. The algorithm can be used to implement global snapshots (?), quick flooding applications, leader election (?), global reset (????), and clock synchronization (???????). In this work, we assumed that an m-wave ends when every process receives a broadcast regardless of whether the input starting the broadcasts in the m-wave are identical or not. Observe that the semantics implemented/required by them-wave changes depending on the input and its arrival pattern in the network. Investigation of the variations in the implementations ofm-wave algorithms depending on input types and patterns, input synchronization requirements, and the desirable semantics are open problems. We are currently devising other m-wave algorithms implementing variations of semantics. Another possible extension of this algorithm allowing each participating initiator to broadcast a sequence of distinct waves, which can be used to implement stabilizing phase clocks, is desirable. In addition, a snap-stabilizing m-wave algorithm for arbitrary networks can be devised.

中文翻译：

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一种用于树网络的稳定 m 波算法

我们提出了一种稳定的 m 波算法，实现了来自树网络的多个发起者的波。所提出的算法保证即使是由发起者启动的第一个 m-wave 也能成功地将消息传递给每个进程。该算法可用于实现全局快照（？）、快速泛洪应用程序、领导者选举（？）、全局重置（????）和时钟同步（???????）。在这项工作中，我们假设 m-wave 在每个进程收到广播时结束，而不管 m-wave 中开始广播的输入是否相同。观察到它们实现/要求的语义会根据输入及其在网络中的到达模式而变化。根据输入类型和模式研究 m-wave 算法实现的变化，输入同步要求和理想的语义是开放问题。我们目前正在设计其他实现语义变化的 m-wave 算法。该算法的另一个可能的扩展是允许每个参与的发起者广播一系列不同的波，这可用于实现稳定的相位时钟。此外，可以设计用于任意网络的快速稳定 m 波算法。