We present a linear program for the one-way version of the partition bound (denoted $\mathsf{prt}^1_\varepsilon(f)$). We show that it characterizes one-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ with shared randomness of every partial function $f:\mathcal{X}\times\mathcal{Y}\to\mathcal{Z}$, i.e., for $\delta,\varepsilon\in(0,1/2)$, $\mathsf{R}_\varepsilon^1(f) \geq \log\mathsf{prt}_\varepsilon^1(f)$ and $\mathsf{R}_{\varepsilon+\delta}^1(f) \leq \log\mathsf{prt}_\varepsilon^1(f) + \log\log(1/\delta)$. This improves upon the characterization of $\mathsf{R}_\varepsilon^1(f)$ in terms of the rectangle bound (due to Jain and Klauck, 2010) by reducing the additive $O(\log(1/\delta))$-term to $\log\log(1/\delta)$.

翻译：我们提出了划分界单向版本（记为 $\mathsf{prt}^1_\varepsilon(f)$）的一个线性规划。我们证明它刻画了每个部分函数 $f:\mathcal{X}\times\mathcal{Y}\to\mathcal{Z}$ 的带共享随机性的单向随机化通信复杂度 $\mathsf{R}_\varepsilon^1(f)$，即对于 $\delta,\varepsilon\in(0,1/2)$，有 $\mathsf{R}_\varepsilon^1(f) \geq \log\mathsf{prt}_\varepsilon^1(f)$ 和 $\mathsf{R}_{\varepsilon+\delta}^1(f) \leq \log\mathsf{prt}_\varepsilon^1(f) + \log\log(1/\delta)$。这改进了基于矩形界的 $\mathsf{R}_\varepsilon^1(f)$ 刻画（归功于Jain和Klauck, 2010），将加性的 $O(\log(1/\delta))$ 项缩减为 $\log\log(1/\delta)$。