Approximation Algorithms for Steiner Connected Dominating Set  

作　　者：Ya-Feng Wu Yin-Long Xu Guo-Liang Chen 

机构地区：[1]National High Performance Computing Center at Hefei, Department of Computer Science and Technology University of Science and Technology of China, Hefei 230027, P.R. China

出　　处：《Journal of Computer Science & Technology》2005年第5期713-716,共4页计算机科学技术学报（英文版）

基　　金：国家自然科学基金，'Research on Routing and Wave length assignment in WDM All-optical Networks'

摘　　要：Steiner connected dominating set （SCDS） is a generalization of the famous connected dominating set problem, where only a specified set of required vertices has to be dominated by a connected dominating set, and known to be NP- hard. This paper firstly modifies the SCDS algorithm of Guha and Khuller and achieves a worst case approximation ratio of （2 ＋ 1/（m - 1））H（min（△, k）） ＋O（1）, which outperforms the previous best result （c ＋ 1）H（min（△, k）） ＋ O（1） in the case of m ≥ 1 ＋1/（c - 1）, where c is the best approximation ratio for Steiner tree, A is the maximum degree of the graph, k is the cardinality of the set of required vertices, m is an optional integer satisfying 0 ≤ m ≤ min（△, k） and H is the harmonic function. This paper also proposes another approximation algorithm which is based on a greedy approach. The second algorithm can establish a worst case approximation ratio of 2 ln（min（△, k）） ＋ O（1）, which can also be improved to 2 lnk if the optimal solution is greater than c·e^2c＋1/2（c＋1）.Steiner connected dominating set （SCDS） is a generalization of the famous connected dominating set problem, where only a specified set of required vertices has to be dominated by a connected dominating set, and known to be NP- hard. This paper firstly modifies the SCDS algorithm of Guha and Khuller and achieves a worst case approximation ratio of （2 ＋ 1/（m - 1））H（min（△, k）） ＋O（1）, which outperforms the previous best result （c ＋ 1）H（min（△, k）） ＋ O（1） in the case of m ≥ 1 ＋1/（c - 1）, where c is the best approximation ratio for Steiner tree, A is the maximum degree of the graph, k is the cardinality of the set of required vertices, m is an optional integer satisfying 0 ≤ m ≤ min（△, k） and H is the harmonic function. This paper also proposes another approximation algorithm which is based on a greedy approach. The second algorithm can establish a worst case approximation ratio of 2 ln（min（△, k）） ＋ O（1）, which can also be improved to 2 lnk if the optimal solution is greater than c·e^2c＋1/2（c＋1）.

关 键 词：approximation algorithm Steiner connected dominated set graph algorithm NP-HARD 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]