紧凑消息传递中的若干问题
Some Problems in Compact Message Passing
摘要：
本文旨在解决的问题，设计分布式算法的设置紧凑的内存，即亚线性位的工作内存为任意连接的网络。我们网络中的节点可能具有比其可能邻居的数量低得多的内部存储器，这意味着节点可能无法存储其邻居的所有ID。这些算法对于诸如物联网之类的小型设备的大型网络、对于无线或自组织网络是有用的，并且通常作为存储器高效算法。我们介绍了紧凑的消息传递（CMP）模型，标准的消息传递模型的扩展，考虑在一个更细的粒度，节点可以交错的读取和写入与内部计算，使用一个端口只有一次在一轮。由于低存储器需求，需要交错来进行有意义的计算，并且交错类似于具有执行流算法的节点的分布式网络。请注意，内部内存大小限制了消息大小的上限，因此例如对于日志内存，该模型比Congest模型弱;对于此类模型，我们的算法也将直接工作。我们给出了具有log^2-记忆节点的CMP模型的早期结果。我们介绍了局部紧函数和紧协议的概念，并给出了一些经典的分布式问题（领导选举，树的建设和遍历）的解决方案。在此基础上，我们通过设计用于查找标记二叉树的特定子树的局部紧凑函数，解决了在自修复树中的紧凑路由消息（TCS 2017）中提出的紧凑自修复路由算法CompactFTZ的紧凑预处理的开放问题。因此，我们介绍了第一个完全紧凑的自愈路由算法。我们还给出了独立的完全紧凑版本的宽恕树[PODC 08]和Thorup-Zwick的基于树的紧凑路由[SPAA 01]。
英文摘要：
This paper seeks to address the question of designing distributed algorithms for the setting of compact memory i.e. sublinear bits working memory for arbitrary connected networks. The nodes in our networks may have much lower internal memory as compared to the number of their possible neighbours implying that a node may not be able to store all the IDs of its neighbours. These algorithms are useful for large networks of small devices such as the Internet of Things, for wireless or ad-hoc networks, and, in general, as memory efficient algorithms. We introduce the Compact Message Passing(CMP) model;an extension of the standard message passing model considered at a finer granularity where a node can interleave reads and writes with internal computations, using a port only once in a round. The interleaving is required for meaningful computations due to the low memory requirement and is akin to a distributed network with nodes executing streaming algorithms. Note that the internal memory size upper bounds the message sizes and hence e.g. for log-memory, the model is weaker than the Congest model; for such models our algorithms will work directly too. We present early results in the CMP model for nodes with log^2-memory. We introduce the concepts of local compact functions and compact protocols and give solutions for some classic distributed problems (leader election, tree constructions and traversals). We build on these to solve the open problem of compact preprocessing for the compact self-healing routing algorithm CompactFTZ posed in Compact Routing Messages in Self-Healing Trees(TCS2017) by designing local compact functions for finding particular subtrees of labeled binary trees. Hence, we introduce the first fully compact self-healing routing algorithm. We also give independent fully compact versions of the Forgiving Tree[PODC08] and Thorup-Zwick's tree based compact routing[SPAA01].
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