On weakly connected domination in graphs
Discrete Mathematics
Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Weakly-Connected Dominating Sets and Sparse Spanners in Wireless Ad Hoc Networks
ICDCS '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
Minimum connected dominating sets and maximal independent sets in unit disk graphs
Theoretical Computer Science
Weakly connected dominating set-based secure clustering and operation in distributed sensor networks
International Journal of Communication Networks and Distributed Systems
Maximum lifetime connected coverage with two active-phase sensors
Journal of Global Optimization
On construction of quality fault-tolerant virtual backbone in wireless networks
IEEE/ACM Transactions on Networking (TON)
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Secure clustering problem plays an important role in distributed sensor networks. Weakly Connected Dominating Set (WCDS) is used for solving this problem. Therefore, computing a minimum WCDS becomes an important topic of this research. In this paper, we compare the size of Maximal Independent Set (MIS) and minimum WCDS in unit disk graph. Our analysis shows that five is the least upper bound for this ratio. We also present a distributed algorithm to produce a weakly connected MIS within a factor 5 from the minimum WCDS.