Efficient Counting and Simulation in Content-Oblivious Rings

2026-03-30

AI Summary

This work investigates efficient distributed counting and asynchronous message-passing simulation in anonymous ring networks under a pulse-based, content-oblivious (CO) communication model. For anonymous rings with a leader and rings with unique identifiers, the paper presents the first counting algorithms whose pulse complexities—O(n^1.5) and O(n log²n), respectively—nearly match the theoretical lower bound of Ω(n log n), which the authors also establish. Building upon this counting primitive, the study further designs a message-passing simulator that incurs only O(b) pulses per simulated round for messages of size b, applicable to any 2-edge-connected network. This approach substantially reduces communication overhead compared to prior methods, demonstrating a significant advance in pulse-efficient distributed computation under stringent anonymity and communication constraints.

Abstract

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.

Problem

• content-oblivious
• counting
• ring topology
• distributed computing
• message efficiency

Innovation

• content-oblivious communication
• pulse-efficient simulation
• distributed counting
• ring topology
• message-passing simulation