## Abstract

We study the task of gathering k energy-constrained mobile agents in an undirected edge-weighted graph. Each agent is initially placed on an arbitrary node and has a limited amount of energy, which constrains the distance it can move. Since this may render gathering at a single point impossible, we study three variants of near-gathering:

The goal is to move the agents into a configuration that minimizes either (i) the radius of a ball containing all agents, (ii) the maximum distance between any two agents, or (iii) the average distance between the agents. We prove that (i) is polynomial-time solvable, (ii) has a polynomial-time 2-approximation with a matching NP-hardness lower bound, while (iii) admits a polynomial-time 2(1 - 1/k)-approximation, but no FPTAS, unless P = NP. We extend some of our results to additive approximation. (C) 2020 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 35-46 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 849 |

DOIs | |

Publication status | Published - 6 Jan 2021 |

## Keywords

- Mobile agents
- Power-aware robots
- Limited battery
- Gathering
- Graph algorithms
- Approximation
- Computational complexity