Efficient Counting and Simulation in Content-Oblivious Rings
This work addresses the inefficiency of distributed algorithms in content-oblivious networks, enabling more practical applications in asynchronous systems, though it is incremental as it builds on prior simulation results.
The paper tackles the problem of inefficient simulation of classical message passing in content-oblivious networks by developing a new simulator that reduces the pulse cost to O(b) per process per round, and provides efficient counting algorithms with O(n^1.5) pulses for anonymous rings and O(n log^2 n) for rings with IDs, along with a lower bound of Ω(n log n).
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.