{"paper":{"title":"Near-Optimal Algorithms for Shortest Paths in Weighted Unit-Disk Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Haitao Wang, Jie Xue","submitted_at":"2019-03-12T23:11:02Z","abstract_excerpt":"We revisit a classical graph-theoretic problem, the \\textit{single-source shortest-path} (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in $O(n \\log^2 n)$ time using linear space, where $n$ is the number of the vertices of the graph. This significantly improves the previous deterministic algorithm by Cabello and Jej\\v{c}i\\v{c} [CGTA'15] which uses $O(n^{1+\\delta})$ time and $O(n^{1+\\delta})$ space (for any small constant $\\delta>0$) and the previous randomized algorithm by Kaplan et al. [SODA'17] which uses $O(n \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05255","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"}