{"paper":{"title":"On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Tung-Wei Kuo","submitted_at":"2017-11-29T04:56:43Z","abstract_excerpt":"In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \\cup \\{u,v\\}$ is at most $\\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\\log n)$-approximation algorithm ($n=|V|$) for $\\alpha = 1$ by Ding et al. For any constant $\\alpha > 1$, we give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10680","kind":"arxiv","version":4},"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"}