{"paper":{"title":"Lossy kernels for connected distance-$r$ domination on nowhere dense graph classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Sebastian Siebertz","submitted_at":"2017-07-31T12:33:49Z","abstract_excerpt":"For $\\alpha\\colon\\mathbb{N}\\rightarrow\\mathbb{R}$, an $\\alpha$-approximate bi-kernel is a polynomial-time algorithm that takes as input an instance $(I, k)$ of a problem $Q$ and outputs an instance $(I',k')$ of a problem $Q'$ of size bounded by a function of $k$ such that, for every $c\\geq 1$, a $c$-approximate solution for the new instance can be turned into a $c\\cdot\\alpha(k)$-approximate solution of the original instance in polynomial time. This framework of \\emph{lossy kernelization} was recently introduced by Lokshtanov et al. We prove that for every nowhere dense class of graphs, every $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09819","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"}