{"paper":{"title":"Parameterized Approximation Algorithms for some Location Problems in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arne Leitert, Feodor F. Dragan","submitted_at":"2017-06-22T19:56:51Z","abstract_excerpt":"We develop efficient parameterized, with additive error, approximation algorithms for the (Connected) $r$-Domination problem and the (Connected) $p$-Center problem for unweighted and undirected graphs. Given a graph $G$, we show how to construct a (connected) $\\big(r + \\mathcal{O}(\\mu) \\big)$-dominating set $D$ with $|D| \\leq |D^*|$ efficiently. Here, $D^*$ is a minimum (connected) $r$-dominating set of $G$ and $\\mu$ is our graph parameter, which is the tree-breadth or the cluster diameter in a layering partition of $G$. Additionally, we show that a $+ \\mathcal{O}(\\mu)$-approximation for the ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07475","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"}