Near-gathering of energy-constrained mobile agents

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

doi:10.1016/j.tcs.2020.10.008

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 journal › Article › Academic › peer-review

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
Pages (from-to)	35-46
Number of pages	12
Journal	Theoretical Computer Science
Volume	849
DOIs	https://doi.org/10.1016/j.tcs.2020.10.008
Publication status	Published - 6 Jan 2021

Keywords

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

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10.1016/j.tcs.2020.10.008

Cite this

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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 - 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.",

keywords = "Mobile agents, Power-aware robots, Limited battery, Gathering, Graph algorithms, Approximation, Computational complexity",

author = "Andreas Baertschi and Evangelos Bampas and Jeremie Chalopin and Shantanu Das and Christina Karousatou and Maths Mihalak",

note = "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. B{\"a}rtschi was working at ETH Z{\"u}rich, and E. Bampas and C. Karousatou were working at Aix-Marseille Universit{\'e}. Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

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AU - Baertschi, Andreas

AU - Bampas, Evangelos

AU - Chalopin, Jeremie

AU - Das, Shantanu

AU - Karousatou, Christina

AU - Mihalak, Maths

N1 - 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. Bärtschi was working at ETH Zürich, and E. Bampas and C. Karousatou were working at Aix-Marseille Université. Publisher Copyright: © 2020 Elsevier B.V.

PY - 2021/1/6

Y1 - 2021/1/6

N2 - 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.

AB - 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.

KW - Mobile agents

KW - Power-aware robots

KW - Limited battery

KW - Gathering

KW - Graph algorithms

KW - Approximation

KW - Computational complexity

U2 - 10.1016/j.tcs.2020.10.008

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JO - Theoretical Computer Science

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