In this paper, we delve into the computations performed at a node within a message-passing algorithm. We investigate low complexity/latency multi-input structures that can be adopted by the node for computing outgoing messages y = (y1, y2, . . . , yn) from incoming messages x = (x1, x2, . . . , xn), where each yj , j = 1, 2, . . . , n is computed via a multi-way tree with leaves x excluding xj . Specifically, we propose two classes of structures for different scenarios. For the scenario where complexity has a higher priority than latency, the star-tree-based structures are proposed. The complexity-optimal ones (as well as their lowest latency) of such structures are obtained, which have the near-lowest (and sometimes the lowest) complexity among all structures. For the scenario where latency has a higher priority than complexity, the isomorphic-directed-rooted-tree-based structures are proposed. The latency-optimal ones (as well as their lowest complexity) of such structures are obtained, which are proved to have the lowest latency among all structures.

翻译：本文深入研究了消息传递算法中节点执行的计算。我们探讨了节点可采用的低复杂度/低延迟多输入结构，用于根据输入消息 x = (x1, x2, ..., xn) 计算输出消息 y = (y1, y2, ..., yn)，其中每个 yj (j = 1, 2, ..., n) 通过一个多路树计算得出，该树的叶节点为除 xj 之外的所有 x。具体而言，我们针对不同场景提出了两类结构。对于复杂度优先于延迟的场景，提出了基于星型树的结构。我们获得了此类结构中复杂度最优（及其最低延迟）的结构，它们在所有结构中具有接近最低（有时是最低）的复杂度。对于延迟优先于复杂度的场景，提出了基于同构有向根树的结构。我们获得了此类结构中延迟最优（及其最低复杂度）的结构，并证明其在所有结构中具有最低的延迟。