On the Performance of Weakly Connected Dominating Set and Loosely Coupled Dominating Set for Wireless Sensor/Mesh Networks

Using an underlying cluster-based virtual backbone induced by the weakly connected dominating set (WCDS) is a very promising approach to enhance network efficiency. This paper proposes a novel loosely-coupled dominating set (LCDS) which is adapted from the concept of WCDS by further relaxing its connectivity requirement. The main advantages of the proposed LCDS are as follows. First, it can further reduce the size of the dominating set compared with that generated by the WCDS. Second, it can decrease the average utilization of the selected cluster heads to prolong their life-cycle. Third, it can increase the edge coverage of the network to exploit the benefits of load balancing. Fourth, it provides the network with high reliability by supporting more alternative routing paths. Numerical results show that the proposed LCDS outperforms the WCDS in almost every node deployment scenarios and every performance aspects.

New Self-Stabilizing Algorithms for Minimal Weakly Connected Dominating Sets

In this paper, we propose two new self-stabilizing algorithms, MWCDS-C and MWCDS-D, for minimal weakly connected dominating sets in an arbitrary connected graph. Algorithm MWCDS-C stabilizes in O(n4) steps using an unfair central daemon and space requirement at each node is O(log n) bits at each node for an arbitrary connected graph with n nodes; it uses a designated node while other nodes are identical and anonymous. Algorithm MWCDS-D stabilizes using an unfair distributed daemon with identical time and space complexities, but it assumes unique node IDs. In the literature, the best reported stabilization time for a minimal weakly connected dominating set algorithm is O(nmA) under a distributed daemon [1], where m is the number of edges and A is the number of moves to construct a breadth-first tree.

LEARNING AUTOMATA-BASED ALGORITHMS FOR FINDING MINIMUM WEAKLY CONNECTED DOMINATING SET IN STOCHASTIC GRAPHS

A weakly connected dominating set (WCDS) of graph G is a subset of G so that the vertex set of the given subset and all vertices with at least one endpoint in the subset induce a connected sub-graph of G. The minimum WCDS (MWCDS) problem is known to be NP-hard, and several approximation algorithms have been proposed for solving MWCDS in deterministic graphs. However, to the best of our knowledge no work has been done on finding the WCDS in stochastic graphs. In this paper, a definition of the MWCDS problem in a stochastic graph is first presented and then several learning automata-based algorithms are proposed for solving the stochastic MWCDS problem where the probability distribution function of the weight associated with the graph vertices is unknown. The proposed algorithms significantly reduce the number of samples needs to be taken from the vertices of the stochastic graph. It is shown that by a proper choice of the parameters of the proposed algorithms, the probability of finding the MWCDS is as close to unity as possible. Experimental results show the major superiority of the proposed algorithms over the standard sampling method in terms of the sampling rate.