{"paper":{"title":"Linear kernels and single-exponential algorithms via protrusion decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Alexander Langer, Christophe Paul, Eun Jung Kim, Felix Reidl, Ignasi Sau, Peter Rossmanith, Somnath Sikdar","submitted_at":"2012-07-03T20:55:53Z","abstract_excerpt":"A \\emph{$t$-treewidth-modulator} of a graph $G$ is a set $X \\subseteq V(G)$ such that the treewidth of $G-X$ is at most some constant $t-1$. In this paper, we present a novel algorithm to compute a decomposition scheme for graphs $G$ that come equipped with a $t$-treewidth-modulator. This decomposition, called a \\emph{protrusion decomposition}, is the cornerstone in obtaining the following two main results.\n  We first show that any parameterized graph problem (with parameter $k$) that has \\emph{finite integer index} and is \\emph{treewidth-bounding} admits a linear kernel on $H$-topological-min"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0835","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"}