Near-Gathering of Energy-Constrained Mobile Agents

  • Andreas BärtschiEmail author
  • Evangelos Bampas
  • Jérémie Chalopin
  • Shantanu Das
  • Christina Karousatou
  • Matúš Mihalák
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11639)


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 \(2(1-\tfrac{1}{k})\)-approximation, but no FPTAS, unless \(\text {P}=\text {NP}\). We extend some of our results to additive approximation.


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


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Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  • Andreas Bärtschi
    • 1
    Email author
  • Evangelos Bampas
    • 2
  • Jérémie Chalopin
    • 3
  • Shantanu Das
    • 3
  • Christina Karousatou
    • 4
  • Matúš Mihalák
    • 5
  1. 1.Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Laboratoire de Recherche en InformatiqueUniversité Paris-SudOrsay CedexFrance
  3. 3.CNRSAix-Marseille Université and Université de Toulon, LISToulonFrance
  4. 4.Department of MathematicsTU DarmstadtDarmstadtGermany
  5. 5.Department of Data Science and Knowledge EngineeringMaastricht UniversityMaastrichtThe Netherlands

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