{"paper":{"title":"A Linear-Time Algorithm for the Weighted Paired-Domination Problem on Block Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cheng-Yu Hsieh, Ching-Chi Lin","submitted_at":"2016-05-02T07:19:17Z","abstract_excerpt":"In a graph $G = (V,E)$, a vertex subset $S\\subseteq V(G)$ is said to be a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A dominating set $S$ of $G$ is called a paired-dominating set of $G$ if the induced subgraph $G[S]$ contains a perfect matching. In this paper, we propose an $O(n+m)$-time algorithm for the weighted paired-domination problem on block graphs using dynamic programming, which strengthens the results in [Theoret. Comput. Sci., 410(47--49):5063--5071, 2009] and [J. Comb. Optim., 19(4):457--470, 2010]. Moreover, the algorithm can be completed in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00372","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"}