{"paper":{"title":"Improved Approximation for Weighted Tree Augmentation with Bounded Costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Adjiashvili","submitted_at":"2016-07-13T15:32:18Z","abstract_excerpt":"The Weighted Tree Augmentation Problem (WTAP) is a fundamental well-studied problem in the field of network design. Given an undirected tree $G=(V,E)$, an additional set of edges $L \\subseteq V\\times V$ disjoint from $E$ called \\textit{links}, and a cost vector $c\\in \\mathbb{R}_{\\geq 0}^L$, WTAP asks to find a minimum-cost set $F\\subseteq L$ with the property that $(V,E\\cup F)$ is $2$-edge connected. The special case where $c_\\ell = 1$ for all $\\ell\\in L$ is called the Tree Augmentation Problem (TAP). Both problems are known to be NP-hard.\n  For the class of bounded cost vectors, we present a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03791","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":""},"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"}