Algorithms for Steiner Connected Dominating Set Problem Based on Learning Automata Theory

Abstract

The Steiner connected dominating set problem is a generalization of the well-known connected dominating set problem, in which only a specified subset of the vertices must be dominated. Finding the Steiner connected dominating set is an NP-hard problem in graph theory, and a new promising approach for multicast routing in wireless ad hoc networks. In this paper, we propose six learning automata-based approximation algorithms for finding a near optimal solution to the minimum Steiner connected dominating set problem. For the first proposed algorithm, it is shown that, by a proper choice of the learning rate of algorithm, the probability of approximating the optimal solution is as close to unity as possible. Moreover, we compute the worst case running time of this algorithm for finding a 1/(1 − ε) optimal solution, and show that, by a proper choice of the learning rate, a trade-off between the running time of algorithm and dominating set size can be made. The last proposed algorithm is compared with the previous well-known algorithms and the results show the superiority of the proposed algorithm both in terms of the dominating set size and running time.