{"paper":{"title":"Polylogarithmic Approximation Algorithms for Weighted-$\\mathcal{F}$-Deletion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Akanksha Agrawal, Daniel Lokshtanov, Meirav Zehavi, Pranabendu Misra, Saket Saurabh","submitted_at":"2017-07-16T16:49:03Z","abstract_excerpt":"For a family of graphs $\\cal F$, the canonical Weighted $\\cal F$ Vertex Deletion problem is defined as follows: given an $n$-vertex undirected graph $G$ and a weight function $w: V(G)\\rightarrow\\mathbb{R}$, find a minimum weight subset $S\\subseteq V(G)$ such that $G-S$ belongs to $\\cal F$. We devise a recursive scheme to obtain $O(\\log^{O(1)}n)$-approximation algorithms for such problems, building upon the classic technique of finding balanced separators in a graph. Roughly speaking, our scheme applies to problems where an optimum solution $S$, together with a well-structured set $X$, form a b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04908","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"}