{"paper":{"title":"Dynamic Deterministic Constant-Approximate Distance Oracles with $n^{\\epsilon}$ Worst-Case Update Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bernhard Haeupler, Thatchaphol Saranurak, Yaowei Long","submitted_at":"2024-02-28T18:24:05Z","abstract_excerpt":"We present a new distance oracle in the fully dynamic setting: given a weighted undirected graph $G=(V,E)$ with $n$ vertices undergoing both edge insertions and deletions, and an arbitrary parameter $\\epsilon$ where $\\epsilon\\in[1/\\log^{c} n,1]$ and $c>0$ is a small constant, we can deterministically maintain a data structure with $n^{\\epsilon}$ worst-case update time that, given any pair of vertices $(u,v)$, returns a $2^{{\\rm poly}(1/\\epsilon)}$-approximate distance between $u$ and $v$ in ${\\rm poly}(1/\\epsilon)\\log\\log n$ query time.\n  Our algorithm significantly advances the state-of-the-a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.18541","kind":"arxiv","version":2},"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/2402.18541/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"}