{"paper":{"title":"Deterministic Approximation of Random Walks via Queries in Graphs of Unbounded Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Edward Pyne, Salil Vadhan","submitted_at":"2021-11-03T03:30:30Z","abstract_excerpt":"Consider the following computational problem: given a regular digraph $G=(V,E)$, two vertices $u,v \\in V$, and a walk length $t\\in \\mathbb{N}$, estimate the probability that a random walk of length $t$ from $u$ ends at $v$ to within $\\pm \\varepsilon.$ A randomized algorithm can solve this problem by carrying out $O(1/\\varepsilon^2)$ random walks of length $t$ from $u$ and outputting the fraction that end at $v$.\n  In this paper, we study deterministic algorithms for this problem that are also restricted to carrying out walks of length $t$ from $u$ and seeing which ones end at $v$. Specifically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.01997","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/2111.01997/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"}