On approximation algorithms of k -connected m -dominating sets in disk graphs

• Published in: Theoretical computer science Vol. 385; no. 1; pp. 49 - 59
• Main Authors: Thai, My T., Zhang, Ning, Tiwari, Ravi, Xu, Xiaochun
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.10.2007; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Computer systems performance. Reliability; Connected dominating set; Disk graphs; Exact sciences and technology; Fault tolerance; Information retrieval. Graph; Miscellaneous; Software; Theoretical computing; Virtual backbone; Wireless ad hoc network; Fault tolerance; Disk graphs; Connected dominating set; Virtual backbone; Wireless ad hoc network; Construction; Approximation; Dominating set; Computer theory; Node; Traffic; Research; Approximation algorithm; Failures; Fault tolerant computing; Network; Broadcasting; Disk; Failure
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2007.05.025

Connected Dominating Set (CDS) has been proposed as the virtual backbone to alleviate the broadcasting storm in wireless ad hoc networks. Most recent research has extensively focused on the construction of 1-Connected 1-Dominating Set (1-CDS) in homogeneous networks. However, the nodes in the CDS need to carry other node’s traffic and nodes in wireless networks are subject to failure. Therefore, it is desirable to construct a fault tolerant CDS. In this paper, we study a general fault tolerant CDS problem, called k -Connected m -Dominating Set ( k - m -CDS), in heterogeneous networks. We first present two approximation algorithms for 1- m -CDS and k - k -CDS problems. Using disk graphs to model heterogeneous networks, we show that our algorithms have a constant approximation ratio. Based on these two algorithms, we further develop a general algorithm for k - m -CDS. We also provide an interesting analysis for a special case of k - m -CDS, where k = m + 1 .