Near-gathering of energy-constrained mobile agents

We study the task of gathering k energy-constrained mobile agents in an undirected edge-weighted graph. Each agent is initially placed on arbitrary node and has a limited amount energy, which constrains distance it can move. Since this may render at single point impossible, we three variants near-gathering: The goal to move into configuration that minimizes either (i) radius ball containing all agents, (ii) maximum between any two or (iii) average agents. prove polynomial-time solvable, 2-approximation with matching NP-hardness lower bound, while admits 2(1−1k)-approximation, but no FPTAS, unless P=NP. extend some our results additive approximation.