A greedy algorithm for the fault-tolerant connected dominating set in a general graph

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• 作者：Jiao Zhou (1)
  Zhao Zhang (1)
  Weili Wu (2)
  Kai Xing (2)
  
• 关键词：$$m$$ m ; fold connected dominating set ; Non ; submodular potential function ; Greedy algorithm
• 刊名：Journal of Combinatorial Optimization
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：28
• 期：1
• 页码：310-319
• 全文大小：
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• 作者单位：Jiao Zhou (1)
  Zhao Zhang (1)
  Weili Wu (2)
  Kai Xing (2)
  
  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, People鈥檚 Republic of China
  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA
  
• ISSN：1573-2886

文摘

Using a connected dominating set (CDS) to serve as the virtual backbone of a wireless network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to an accidental damage or energy depletion, it is desirable that the virtual backbone is fault tolerant. A node set \(C\) is an \(m\) -fold connected dominating set ( \(m\) -fold CDS) of graph \(G\) if every node in \(V(G)\setminus C\) has at least \(m\) neighbors in \(C\) and the subgraph of \(G\) induced by \(C\) is connected. In this paper, we will present a greedy algorithm to compute an \(m\) -fold CDS in a general graph, which has size at most \(2+\ln (\Delta +m-2)\) times that of a minimum \(m\) -fold CDS, where \(\Delta \) is the maximum degree of the graph. This result improves on the previous best known performance ratio of \(2H(\Delta +m-1)\) for this problem, where \(H(\cdot )\) is the Harmonic number.