In the content-oblivious (CO) model (proposed by Censor-Hillel et al.), processes inhabit an asynchronous network and communicate only by exchanging pulses. A series of works has clarified the computational power of this model. In particular, it was shown that, when a leader is present and the network is 2-edge-connected, content-oblivious communication can simulate classical asynchronous message passing. Subsequent results extended this equivalence to leaderless oriented and unoriented rings, and, under non-uniform assumptions, to general 2-edge-connected networks. The simulator of Censor-Hillel et al. requires $O(n^3b+n^3\log n)$ pulses to emulate the send of a single $b$-bit message, making it impractical even on modest-size networks. We focus on message-efficient computation in CO networks. We study the fundamental problem of counting in ring topologies, both because knowing the exact network size is a basic prerequisite for many distributed tasks and because counting immediately implies a broad class of aggregation primitives. We give an algorithm that counts using $O(n^{1.5})$ pulses in anonymous rings with a leader, an $O(n\log^2 n)$ algorithm for counting in rings with IDs. Moreover, we show that any counting algorithm in CO requires $Ω(n\log n)$ pulses. Interestingly, in the course of this investigation, we design a simulator for classic message passing: in one simulated round, each process can send a $b$-bit message to each of its neighbors using only $O(b)$ pulses per process. The simulator extends to general 2-edge-connected networks, after a pre-processing step that requires $O(n^{8}\log n)$ pulses, where $n$ is the number of processes, allowing thus efficient simulation of asynchronous message passing in general 2-edge-connected networks.

翻译：在内容无感知（CO）模型（由Censor-Hillel等人提出）中，进程驻扎于异步网络内，仅通过交换脉冲进行通信。一系列工作已阐明了该模型的计算能力。特别是，研究表明，当存在领导者且网络为2边连通时，内容无感知通信可模拟经典异步消息传递。后续结果将该等价性扩展至无领导者的定向及非定向环，并在非均匀假设下扩展至一般2边连通网络。Censor-Hillel等人的模拟器需要$O(n^3b+n^3\log n)$个脉冲来模拟单条$b$位消息的发送，即使在中等规模网络中也显失实际可行性。我们聚焦于CO网络中的消息高效计算。研究环拓扑中的计数这一基础问题，既因知晓确切网络规模是许多分布式任务的基本前提，也因计数可直接推导出广泛一类聚合原语。我们给出一种算法，在含领导者的匿名环中使用$O(n^{1.5})$个脉冲完成计数，并给出一种适用于含ID环的$O(n\log^2 n)$计数算法。此外，我们证明CO中任何计数算法均需$\Omega(n\log n)$个脉冲。有趣的是，在此研究过程中，我们设计了一款经典消息传递模拟器：在单轮模拟中，每个进程可向各邻居发送一条$b$位消息，且每个进程仅需$O(b)$个脉冲。该模拟器可扩展至一般2边连通网络，仅需在预处理步骤中消耗$O(n^{8}\log n)$个脉冲（其中$n$为进程数），从而在一般2边连通网络中实现异步消息传递的高效模拟。