{"paper":{"title":"A fast algorithm for All-Pairs-Shortest-Paths suitable for neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"cs.DS","authors_text":"Markus Meister, Zeyu Jing","submitted_at":"2023-08-06T05:43:24Z","abstract_excerpt":"Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given by the adjacency matrix $A_{ij}$ then with a suitably small value of $\\gamma$ the shortest path distances are\n  $$ D_{ij} = \\operatorname{ceil} \\left( \\log_{\\gamma} {\\left[ {\\left({\\mathbf{I}}-\\gamma {\\mathbf{A}}\\right)^{-1}} \\right]}_{ij} \\right)$$\n  We derive several graph-theoretic bounds on the value of $\\gamma$, and explore its useful range with numeric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07403","kind":"arxiv","version":2},"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/2308.07403/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"}