Collecting information by power-aware mobile agents

A set of identical, mobile agents is deployed in a weighted network. Each agent possesses a battery - a power source allowing the agent to move along network edges. Agents use their batteries proportionally to the distance traveled. At the beginning, each agent has its initial information. Agents exchange the actually possessed information when they meet. The agents collaborate in order to perform an efficient convergecast , where the initial information of all agents must be eventually transmitted to some agent. The objective of this paper is to investigate what is the minimal value of power, initially available to all agents, so that convergecast may be achieved. We study the question in the centralized and the distributed settings. In the distributed setting every agent has to perform an algorithm being unaware of the network. We give a linear-time centralized algorithm solving the problem for line networks. We give a 2-competitive distributed algorithm achieving convergecast for tree networks. The competitive ratio of 2 is proved to be the best possible for this problem, even if we only consider line networks. We show that already for the case of tree networks the centralized problem is strongly NP-complete. We give a 2-approximation centralized algorithm for general graphs.