{"paper":{"title":"A Note on the Complexity of Computing the Number of Reachable Vertices in a Digraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Michele Borassi","submitted_at":"2016-02-05T19:31:09Z","abstract_excerpt":"In this work, we consider the following problem: given a digraph $G=(V,E)$, for each vertex $v$, we want to compute the number of vertices reachable from $v$. In other words, we want to compute the out-degree of each vertex in the transitive closure of $G$. We show that this problem is not solvable in time $\\mathcal{O}\\left(|E|^{2-\\epsilon}\\right)$ for any $\\epsilon>0$, unless the Strong Exponential Time Hypothesis is false. This result still holds if $G$ is assumed to be acyclic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02129","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":""},"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"}