{"paper":{"title":"Parameterized Complexity of Bandwidth on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Daniel Lokshtanov, Markus Sortland Dregi","submitted_at":"2014-04-30T17:44:03Z","abstract_excerpt":"The bandwidth of a $n$-vertex graph $G$ is the smallest integer $b$ such that there exists a bijective function $f : V(G) \\rightarrow \\{1,...,n\\}$, called a layout of $G$, such that for every edge $uv \\in E(G)$, $|f(u) - f(v)| \\leq b$. In the {\\sc Bandwidth} problem we are given as input a graph $G$ and integer $b$, and asked whether the bandwidth of $G$ is at most $b$. We present two results concerning the parameterized complexity of the {\\sc Bandwidth} problem on trees.\n  First we show that an algorithm for {\\sc Bandwidth} with running time $f(b)n^{o(b)}$ would violate the Exponential Time H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7810","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"}