Yi Jun Chang

Jérémie Chalopin, Yi-Jun Chang, Giuseppe Antonio Di Luna et al.

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.

Yi-Jun Chang, Yanyu Chen, Dipan Dey et al.

We investigate the \emph{minimum weight cycle (MWC)} problem in the $\mathsf{CONGEST}$ model of distributed computing. For undirected weighted graphs, we design a randomized algorithm that achieves a $(k+1)$-approximation, for any \emph{real} number $k \ge 1$. The round complexity of algorithm is \[ \tilde{O}\!\Big( n^{\frac{k+1}{2k+1}} + n^{\frac{1}{k}} + D\, n^{\frac{1}{2(2k+1)}} + D^{\frac{2}{5}} n^{\frac{2}{5}+\frac{1}{2(2k+1)}} \Big). \] where $n$ denotes the number of nodes and $D$ is the unweighted diameter of the graph. This result yields a smooth trade-off between approximation ratio and round complexity. In particular, when $k \geq 2$ and $D = \tilde{O}(n^{1/4})$, the bound simplifies to \[ \tilde{O}\!\left( n^{\frac{k+1}{2k+1}} \right) \] On the lower bound side, assuming the Erdős girth conjecture, we prove that for every \emph{integer} $k \ge 1$, any randomized $(k+1-ε)$-approximation algorithm for MWC requires \[ \tildeΩ\!\left( n^{\frac{k+1}{2k+1}} \right) \] rounds. This lower bound holds for both directed unweighted and undirected weighted graphs, and applies even to graphs with small diameter $D = Θ(\log n)$. Taken together, our upper and lower bounds \emph{match up to polylogarithmic factors} for graphs of sufficiently small diameter $D = \tilde{O}(n^{1/4})$ (when $k \geq 2$), yielding a nearly tight bound on the distributed complexity of the problem. Our results improve upon the previous state of the art: Manoharan and Ramachandran (PODC~2024) demonstrated a $(2+ε)$-approximation algorithm for undirected weighted graphs with round complexity $\tilde{O}(n^{2/3}+D)$, and proved that for any arbitrarily large number $α$, any $α$-approximation algorithm for directed unweighted or undirected weighted graphs requires $Ω(\sqrt{n}/\log n)$ rounds.