Recent work of Sawettamalya and Yu (FOCS 2026) initiated the study of \emph{gap-majority} composition in randomized communication. They showed that if computing a $\{\pm 1\}$-valued function $f$ in $r$ rounds requires $I$ bits of information, then distinguishing whether $\sum_{i=1}^n f(X_i,Y_i)$ is at least $0.01\sqrt{...
A $\Omega(\log\log n) bit lower bound for the constant error-rate regime, and a $\Omega(1/\delta)$ bit lower bound for arbitrarily small error rates, as well as a tight one-way protocol using $O(\log\log n + \log(1/\delta))$ bits of communication.
This work proves an information-theoretically optimal gap-majority lemma in the two-player randomized communication model and makes GapMAJ, to the knowledge, only the third explicit outer gadget that admits a strong composition theorem in the two-player communication setting, following the identity and XOR gadgets.
A new $\widetilde{O}(n^{3/2})$-bit protocol for computing a maximum matching in general graphs and a new $\widetilde{O}(n)$-bit protocol for negative-cycle detection and negative-weight single-source shortest paths are introduced.
Yu Cheng, Tianle Jiang, Pachara Sawettamalya et al.· Embedded Systems and Applica...· 0 citations
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