{"paper":{"title":"An Improved Randomized Data Structure for Dynamic Graph Connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Zhengyu Wang","submitted_at":"2015-10-15T15:41:36Z","abstract_excerpt":"We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\\log^3 n)$ per edge insertion, $O(\\log^4 n)$ per edge deletion, and $O(\\log n/\\log\\log n)$ per query, where $n$ is the number of vertices. The previous best algorithm has worst case running time $O(\\log^4 n)$ per edge insertion and $O(\\log^5 n)$ per edge deletion. The improvement is made by reducing the randomness used in the previous result, so that we save a $\\log n$ factor in update time.\n  Specifically, \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04590","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"}