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題名:	On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint
作者:	郭桐惟 Tung-Wei Kuo
貢獻者:	資科系
關鍵詞:	Connected dominating set; Spanner; Set cover with pairs; MIN-REP problem
日期:	2019-02
上傳時間:	2020-04-28 13:50:37 (UTC+8)
摘要:	In the problem of minimum connected dominating set with routing cost constraint, we are given a graph G=(V,E)G=(V,E) and a positive integer αα, 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∪{u,v}D∪{u,v} is at most αα times that in G. For general graphs, the only known previous approximability result is an O(logn)O(log⁡n)-approximation algorithm (n=\|V\|n=\|V\|) for α=1α=1 by Ding et al. For any constant α>1α>1, we give an O(n1−1α(logn)1α)O(n1−1α(log⁡n)1α)-approximation algorithm. When α≥5α≥5, we give an O(n−−√logn)O(nlog⁡n)-approximation algorithm. Finally, we prove that, when α=2α=2, unless NP⊆DTIME(npolylogn)NP⊆DTIME(npolylog⁡n), for any constant ϵ>0ϵ>0, the problem admits no polynomial-time 2log1−ϵn2log1−ϵ⁡n-approximation algorithm, improving upon the Ω(logδ)Ω(log⁡δ) bound by Du et al., where δδ is the maximum degree of G (albeit under a stronger hardness assumption).
關聯:	International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2018: Algorithms for Sensor Systems pp 32-46
資料類型:	conference
DOI 連結:	https://doi.org/10.1007/978-3-030-14094-6_3
DOI:	10.1007/978-3-030-14094-6_3
顯示於類別:	[資訊科學系] 期刊論文

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