HYBRID分布式模型中的通用最优信息传播与最短路径
Universally Optimal Information Dissemination and Shortest Paths in the HYBRID Distributed Model
AI总结：
本研究聚焦HYBRID分布式模型，提出该模型下首批信息传播与最短路径问题的通用最优算法，定义新图参数邻域质量刻画问题固有复杂度，同时给出匹配所有k值下界的k源最短路径存在性最优算法。
摘要：
在本研究中，我们探讨由Augustine、Hinnenthal、Kuhn、Scheideler和Schneider（SODA 2020）近期提出的分布式计算HYBRID模型，该模型中的节点可使用两种不同的通信模式：沿图边进行的高带宽本地通信，以及低带宽全对全通信，精准体现了现代通信网络的非均匀特性。\n 此前针对HYBRID模型的研究主要聚焦于证明存在性最优算法，即存在一类极端实例，任何算法在这类实例上的性能都无法更优。但这类研究忽略了一个事实：这类最坏情况实例在实际场景中通常不会出现，或是可以被主动规避。在本研究中，我们聚焦于由Garay、Kutten和Peleg（FOCS 1993）首次提出的通用最优性概念。粗略来说，通用最优算法指的是，对于任意输入图，其运行速度都能与专门为该图设计的最优算法相当。\n 我们提出了HYBRID模型下的首批通用最优算法。我们针对HYBRID模型中的基础信息传播任务（例如多消息广播和单播）给出了通用最优解决方案。此外，我们将这些工具加以应用，得到了HYBRID模型中各类最短路径问题的通用最优解。\n 本研究的一项核心概念贡献是提出了一个名为邻域质量（neighborhood quality）的新图参数，该参数能够刻画HYBRID模型中诸多基础图问题的固有复杂度。\n 我们还提出了HYBRID模型下新的存在性最优最短路径算法，这些算法既是我们通用最优算法中的关键子例程，本身也具备独立研究价值。我们针对k源最短路径提出的新算法，对于所有k值都匹配了已有的$\tildeΩ(\frac{k})$下界。此前，该下界仅在$k \tildeΩ(n^{2/3})$时被证明是紧的。
英文摘要：
In this work we consider the HYBRID model of distributed computing, introduced recently by Augustine, Hinnenthal, Kuhn, Scheideler, and Schneider (SODA 2020), where nodes have access to two different communication modes: high-bandwidth local communication along the edges of the graph and low-bandwidth all-to-all communication, capturing the non-uniform nature of modern communication networks. Prior work in HYBRID has focused on showing existentially optimal algorithms, meaning there exists a pathological family of instances on which no algorithm can do better. This neglects the fact that such worst-case instances often do not appear or can be actively avoided in practice. In this work, we focus on the notion of universal optimality, first raised by Garay, Kutten, and Peleg (FOCS 1993). Roughly speaking, a universally optimal algorithm is one that, given any input graph, runs as fast as the best algorithm designed specifically for that graph. We show the first universally optimal algorithms in HYBRID. We present universally optimal solutions for fundamental information dissemination tasks, such as broadcasting and unicasting multiple messages in HYBRID. Furthermore, we apply these tools to obtain universally optimal solutions for various shortest paths problems in HYBRID. A main conceptual contribution of this work is the conception of a new graph parameter called neighborhood quality that captures the inherent complexity of many fundamental graph problems in HYBRID. We also show new existentially optimal shortest paths algorithms in HYBRID, which are utilized as key subroutines in our universally optimal algorithms and are of independent interest. Our new algorithms for $k$-source shortest paths match the existing $\tildeΩ(\sqrt{k})$ lower bound for all $k$. Previously, the lower bound was only known to be tight when $k \in \tildeΩ(n^{2/3})$.
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