Communication Problems for Mobile Agents Exchanging Energy
A set of mobile agents is deployed in the nodes of an edge-weighted network. Agents originally possess amounts of energy, possibly different for all agents. The agents travel in the network spending energy proportional to the distance traversed. Some nodes of the network may keep information which is acquired by the agents visiting them. The meeting agents may exchange currently possessed information, as well as any amount of energy. We consider communication problems when the information initially held by some network nodes have to be communicated to some other nodes and/or agents. The paper deals with two communication problems: data delivery and convergecast. These problems are posed for a centralized scheduler which has full knowledge of the instance. It is already known that, without energy exchange, both problems are NP-complete even if the network is a line. In this paper we show that, if the agents are allowed to exchange energy, both problems have linear-time solutions on trees. On the other hand for general undirected and directed graphs we show that these problems are NP-complete.
Research of the second, fourth and (in part) the first author is supported by the grant NCN2014/13/B/ST6/00770 of the Polish National Science Center. Research of the first and the third author is supported in part by NSERC Discovery grant.
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