@inbook{5861e2677b874cdaa5c482dc3c0b2476,

title = "Near-Gathering of Energy-Constrained Mobile Agents",

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 \(2(1-\tfrac{1}{k})\)-approximation, but no fptas, unless \(\text {p}=\text {np}\). We extend some of our results to additive approximation.keywordsmobile agentspower-aware robotslimited batterygatheringgraph algorithmsapproximationcomputational complexity.",

author = "Andreas B{\"a}rtschi and Evangelos Bampas and J{\'e}r{\'e}mie Chalopin and Shantanu Das and Christina Karousatou and Mat{\'u}s Mihal{\'a}k",

note = "Funding Information: Keywords: Mobile agents · Power-aware robots · Limited battery · Gathering · Graph algorithms · Approximation · Computational complexity This work was partially supported by the SNF (project 200021L 156620) and by the ANR (project ANCOR anr-14-CE36-0002-01), while A. B{\"a}rtschi was working at ETH Z{\"u}rich, and E. Bampas and C. Karousatou were working at Aix-Marseille Universit{\'e}. The Los Alamos National Laboratory report number is LA-UR-19-23906. Funding Information: This work was partially supported by the SNF (project 200021L_156620) and by the ANR (project ANCOR anr-14-CE36-0002-01), while A. Bartschi was working at ETH Zurich, and E.Bampas and C. Karousatou were working at Aix-Marseille Universit?. The Los Alamos National Laboratory report number is LA-UR-19-23906. Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.",

year = "2019",

doi = "10.1007/978-3-030-24922-9_4",

language = "English",

series = "Lecture Notes in Computer Science",

publisher = "Springer, Cham",

number = "11639",

pages = "52--65",

editor = "Keren Censor-Hillel and Michele Flammini",

booktitle = "Structural Information and Communication Complexity",

address = "Switzerland",

}