Near-gathering of energy-constrained mobile agents

Andreas Baertschi*, Evangelos Bampas, Jeremie Chalopin, Shantanu Das, Christina Karousatou, Maths Mihalak

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)35-46
Number of pages12
JournalTheoretical Computer Science
Publication statusPublished - 6 Jan 2021


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


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