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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:	2019-11
上傳時間:	2020-04-28 13:50:21 (UTC+8)
摘要:	In the problem of minimum connected dominating set with routing cost constraint, we are given a graph \\(G=(V,E)\\) and a positive integer \\(\\alpha \\), 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 an \\(O(n^{1-\\frac{1}{\\alpha }}(\\log n)^{\\frac{1}{\\alpha }})\\)-approximation algorithm. When \\(\\alpha \\ge 5\\), we give an \\(O(\\sqrt{n}\\log n)\\)-approximation algorithm. Finally, we prove that, when \\(\\alpha =2\\), unless \\(NP \\subseteq DTIME(n^{poly\\log n})\\), for any constant \\(\\epsilon > 0\\), the problem admits no polynomial-time \\(2^{\\log ^{1-\\epsilon }n}\\)-approximation algorithm, improving upon the \\(\\varOmega (\\log \\delta )\\) bound by Du et al., where \\(\\delta \\) is the maximum degree of G (albeit under a stronger hardness assumption).
關聯:	Theoretical Computer Science, Vol.793, pp.140 - 151
資料類型:	article
DOI 連結:	https://doi.org/10.1016/j.tcs.2019.06.019
DOI:	10.1016/j.tcs.2019.06.019
顯示於類別:	[資訊科學系] 期刊論文

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