Data Delivery by Mobile Agents with Energy Constraints over a fixed path

We consider $k$ mobile agents of limited energy that are initially located at vertices of an edge-weighted graph $G$ and have to collectively deliver data from a source vertex $s$ to a target vertex $t$. The data are to be collected by an agent reaching $s$, who can carry and then hand them over another agent etc., until some agent with the data reaches $t$. The data can be carried only over a fixed $s-t$ path of $G$; each agent has an initial energy budget and each time it passes an edge, it consumes the edge's weights in energy units and stalls if its energy is not anymore sufficient to move. The main result of this paper is a 3-approximation polynomial time algorithm for the data delivery problem over a fixed $s-t$ path in the graph, for identical initial energy budgets and at most one allowed data hand-over per agent.