{"paper":{"title":"Almost Optimal Multiple Source Shortest Paths and Reachability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Barna Saha, Christopher Ye, Yinzhan Xu","submitted_at":"2026-06-25T03:02:46Z","abstract_excerpt":"Given a graph, computing distances and reachabilities from a small set of vertices to the whole graph is an important primitive both in theory and in practice.\n  In undirected unweighted graphs, while computing single-source shortest path (SSSP) requires $O(n^2)$ time in dense graphs, all-pairs shortest paths (APSP) can be computed in $\\hat{O}(n^\\omega) = O(n^{2.372})$ time [Seidel '95] providing significant savings over running $n$ SSSP instances separately. However, if one needs to compute multiple-source shortest paths (MSSP) from a set of $n^\\sigma$ vertices, the previously best known runn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26554","kind":"arxiv","version":1},"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/2606.26554/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"}