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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 28-四月-2020 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 https://doi.org/10.1016/j.tcs.2019.06.019
dc.contributor 資科系
dc.creator (作者) 郭桐惟
dc.creator (作者) Tung-Wei Kuo
dc.date (日期) 2019-11
dc.date.accessioned 28-四月-2020 13:50:21 (UTC+8)-
dc.date.available 28-四月-2020 13:50:21 (UTC+8)-
dc.date.issued (上傳時間) 28-四月-2020 13:50:21 (UTC+8)-
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=148384-
dc.description.abstract (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).
dc.format.extent 2541917 bytes-
dc.format.mimetype application/pdf-
dc.relation (關聯) Theoretical Computer Science, Vol.793, pp.140 - 151
dc.subject (關鍵詞) Connected dominating set ;  Spanner ;  Set cover with pairs ;  MIN-REP problem 
dc.title (題名) On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint
dc.type (資料類型) article
dc.identifier.doi (DOI) 10.1016/j.tcs.2019.06.019
dc.doi.uri (DOI) https://doi.org/10.1016/j.tcs.2019.06.019