Run for Cover: Dominating Set via Mobile Agents

Research involving computing with mobile agents is a fast-growing field, given the advancement of technology in automated systems, e.g., robots, drones, self-driving cars, etc. Therefore, it is pressing to focus on solving classical network problems using mobile agents. In this paper, we study one such problem -- finding small dominating sets of a graph G using mobile agents. Dominating set is interesting in the field of mobile agents as it opens up a way for solving various robotic problems, e.g., guarding, covering, facility location, transport routing, etc. In this paper, we first present two algorithms for computing a em minimal dominating set: (i) an O(m) time algorithm if the robots start from a single node (i.e., gathered initially), (ii) an O(ℓDeltalog(λ)+nℓ+m) time algorithm, if the robots start from multiple nodes (i.e., positioned arbitrarily), where m is the number of edges and Delta is the maximum degree of G, ℓ is the number of clusters of the robot initially and λ is the maximum ID-length of the robots. Then we present a ln (Delta) approximation algorithm for the em minimum dominating set which takes O(nDeltalog (λ)) rounds.