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Time-Energy Tradeoffs for Evacuation by Two Robots in the Wireless Model

  • Jurek Czyzowicz
  • Konstantinos Georgiou
  • Ryan Killick
  • Evangelos KranakisEmail author
  • Danny Krizanc
  • Manuel Lafond
  • Lata Narayanan
  • Jaroslav Opatrny
  • Sunil Shende
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11639)

Abstract

Two robots stand at the origin of the infinite line and are tasked with searching collaboratively for an exit at an unknown location on the line. They can travel at maximum speed b and can change speed or direction at any time. The two robots can communicate with each other at any distance and at any time. The task is completed when the last robot arrives at the exit and evacuates. We study time-energy tradeoffs for the above evacuation problem. The evacuation time is the time it takes the last robot to reach the exit. The energy it takes for a robot to travel a distance x at speed s is measured as \(xs^2\). The total and makespan evacuation energies are respectively the sum and maximum of the energy consumption of the two robots while executing the evacuation algorithm.

Assuming that the maximum speed is b, and the evacuation time is at most cd, where d is the distance of the exit from the origin, we study the problem of minimizing the total energy consumption of the robots. We prove that the problem is solvable only for \(bc \ge 3\). For the case \(bc=3\), we give an optimal algorithm, and give upper bounds on the energy for the case \(bc>3\).

We also consider the problem of minimizing the evacuation time when the available energy is bounded by \(\varDelta \). Surprisingly, when \(\varDelta \) is a constant, independent of the distance d of the exit from the origin, we prove that evacuation is possible in time \(O(d^{3/2}\log d)\), and this is optimal up to a logarithmic factor. When \(\varDelta \) is linear in d, we give upper bounds on the evacuation time.

Keywords

Energy Evacuation Linear Robot Speed Time Trade-offs Wireless communication 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jurek Czyzowicz
    • 1
  • Konstantinos Georgiou
    • 2
  • Ryan Killick
    • 3
  • Evangelos Kranakis
    • 3
    Email author
  • Danny Krizanc
    • 4
  • Manuel Lafond
    • 5
  • Lata Narayanan
    • 6
  • Jaroslav Opatrny
    • 6
  • Sunil Shende
    • 7
  1. 1.Départemant d’informatiqueUniversité du Québec en OutaouaisGatineauCanada
  2. 2.Department of MathematicsRyerson UniversityTorontoCanada
  3. 3.School of Computer ScienceCarleton UniversityOttawaCanada
  4. 4.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  5. 5.Department of Computer ScienceUniversité de SherbrookeSherbrookeCanada
  6. 6.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada
  7. 7.Department of Computer ScienceRutgers UniversityCamdenUSA

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