{"paper":{"title":"Dynamic DFS Tree in Undirected Graphs: breaking the $O(m)$ barrier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Keerti Choudhary, Shahbaz Khan, Shreejit Ray Chaudhury, Surender Baswana","submitted_at":"2015-02-09T13:36:20Z","abstract_excerpt":"Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We address the problem of maintaining a DFS tree when the graph is undergoing {\\em updates} (insertion and deletion of vertices or edges). We present the following results for this problem.\n  (a) Fault tolerant DFS tree: There exists a data structure of size ${O}(m ~polylog~ n)$ such that given any set ${\\cal F}$ of failed vertices or edges, a DFS tree of the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02481","kind":"arxiv","version":4},"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"}