{"paper":{"title":"Space-Efficient DFS and Applications: Simpler, Leaner, Faster","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Torben Hagerup","submitted_at":"2018-05-30T08:56:47Z","abstract_excerpt":"The problem of space-efficient depth-first search (DFS) is reconsidered. A particularly simple and fast algorithm is presented that, on a directed or undirected input graph $G=(V,E)$ with $n$ vertices and $m$ edges, carries out a DFS in $O(n+m)$ time with $n+\\sum_{v\\in V_{\\ge 3}}\\lceil{\\log_2(d_v-1)}\\rceil\n  +O(\\log n)\\le n+m+O(\\log n)$ bits of working memory, where $d_v$ is the (total) degree of $v$, for each $v\\in V$, and $V_{\\ge 3}=\\{v\\in V\\mid d_v\\ge 3\\}$. A slightly more complicated variant of the algorithm works in the same time with at most $n+({4/5})m+O(\\log n)$ bits. It is also shown "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11864","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"}