{"paper":{"title":"Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Lee-Ad Gottlieb, Yair Bartal","submitted_at":"2019-04-07T09:17:30Z","abstract_excerpt":"We give an algorithm that computes a $(1+\\epsilon)$-approximate Steiner forest in near-linear time $n \\cdot 2^{(1/\\epsilon)^{O(ddim^2)} (\\log \\log n)^2}$. This is a dramatic improvement upon the best previous result due to Chan et al., who gave a runtime of $n^{2^{O(ddim)}} \\cdot 2^{(ddim/\\epsilon)^{O(ddim)} \\sqrt{\\log n}}$.\n  For Steiner tree our methods achieve an even better runtime $n (\\log n)^{(1/\\epsilon)^{O(ddim^2)}}$ in doubling spaces. For Euclidean space the runtime can be reduced to $2^{(1/\\epsilon)^{O(d^2)}} n \\log n$, improving upon the result of Arora in fixed dimension $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03611","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"}