{"paper":{"title":"Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part I: Stemless TAP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Joe Cheriyan, Zhihan Gao","submitted_at":"2015-08-29T20:48:09Z","abstract_excerpt":"In Part I, we study a special case of the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. In the special case, we forbid so-called stems; these are a particular type of subtree configuration. For stemless TAP, we prove that the integrality ratio of an SDP relaxation (the Lasserre tightening of an LP relaxation) is $\\leq \\frac{3}{2}+\\epsilon$, where $\\epsilon>0$ can be any small constant. We obtain this result by designing a polynomial-time algorithm for stemless TAP that achieves an approximation guarantee of ($\\frac32+\\epsilon$) relative to the SDP relaxat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07504","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"}