New Biology Inspired Anonymous Distributed Algorithms to Compute Dominating and Total Dominating Sets in Network Graphs

The selection mechanism of sensory organ precursor(SOP) from pre-neural cells of fruity fly has recently been used to develop a new computing paradigm for probabilistic (randomized) distributed algorithms for graph theoretic primitives like maximal independent set (MIS) in networks. The new paradigm is significantly different from the settings of traditional distributed algorithms: nodes are anonymous, the nodes do not need any knowledge of its neighbors, they receive binary message(s) from the neighbor(s), there is no need to decipher the message, only receipt or non-receipt of message(s) at any step of the algorithm. In this paper, we develop two new simple distributed algorithms to compute the minimal dominated set (MDS) and minimal total dominating set (MTDS) in a graph using this new paradigm. We show that the two algorithms for computing the MDS and MTDS respectively converge with probability (1 -- n½) using O(D log n) expected number of steps, where n is the number of nodes in the system and D is the maximum degree of a node. Preliminary experimental simulation results show that the algorithms converge in substantially less number of steps to converge than estimated by the analysis for a large number of graph families.