{"paper":{"title":"A Class of Optimal Structures for Node Computations in Message Passing Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AR","math.IT"],"primary_cat":"cs.IT","authors_text":"Kui Cai, Liang Zhou, Xuan He","submitted_at":"2020-09-05T13:52:01Z","abstract_excerpt":"Consider the computations at a node in a message passing algorithm. Assume that the node has incoming and outgoing messages $\\mathbf{x} = (x_1, x_2, \\ldots, x_n)$ and $\\mathbf{y} = (y_1, y_2, \\ldots, y_n)$, respectively. In this paper, we investigate a class of structures that can be adopted by the node for computing $\\mathbf{y}$ from $\\mathbf{x}$, where each $y_j, j = 1, 2, \\ldots, n$ is computed via a binary tree with leaves $\\mathbf{x}$ excluding $x_j$. We make three main contributions regarding this class of structures. First, we prove that the minimum complexity of such a structure is $3n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02535","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.02535/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}