Evacuation from a Disc in the Presence of a Faulty Robot

Czyzowicz, Jurek; Georgiou, Konstantinos; Godon, Maxime; Kranakis, Evangelos; Kriz̧anc, Danny; Rytter, Wojciech; Włodarczyk, Michał

doi:10.1007/978-3-319-72050-0_10

Cited by 36 publications

(27 citation statements)

References 23 publications

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“…Recently, Brandt et al [6] considered the evacuation problem for k robots on m concurrent rays under the wireless model. Finally, the evacuation problem on a disk with three robots at most one of which is faulty was recently studied by Czyzowicz et al [12], the case of several exit on a disk with two robots was considered in [10], and the priority evacuation of a specific robot in [13], all these under the wireless model.…”

Section: Introductionmentioning

confidence: 99%

Evacuating equilateral triangles and squares in the face-to-face model

Chuangpishit

Mehrabi

Narayanan

et al. 2020

Computational Geometry

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Consider k robots initially located at a point inside a region T . Each robot can move anywhere in T independently of other robots with maximum speed one. The goal of the robots is to evacuate T through an exit at an unknown location on the boundary of T . The objective is to minimize the evacuation time, which is defined as the time the last robot reaches the exit. We consider the face-to-face communication model for the robots: a robot can communicate with another robot only when they meet in T .In this paper, we give upper and lower bounds for the face-to-face evacuation time by k robots that are initially located at the centroid of a unit-sided equilateral triangle or square. For the case of a triangle with k = 2 robots, we give a lower bound of 1 + 2/ √ 3 ≈ 2.154, and an algorithm with upper bound of 2.3367 on the worst-case evacuation time. We show that for any k, any algorithm for evacuating k ≥ 2 robots requires at least √ 3 time. This bound is asymptotically optimal, as we show that even a straightforward strategy of evacuation by k robots gives an upper bound of √ 3 + 3/k. For k = 3 and 4, we give better algorithms with evacuation times of 2.0887 and 1.9816, respectively. For the case of the square and k = 2, we give an algorithm with evacuation time of 3.4645 and show that any algorithm requires time at least 3.118 to evacuate in the worst-case. Moreover, for k = 3, and 4, we give algorithms with evacuation times 3.1786 and 2.6646, respectively. The algorithms given for k = 3 and 4 for evacuation in the triangle or the square can be easily generalized for larger values of k. * A preliminary version of this paper appeared in

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Section: Introductionmentioning

confidence: 99%

Evacuating equilateral triangles and squares in the face-to-face model

Chuangpishit

Mehrabi

Narayanan

et al. 2020

Computational Geometry

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“…Lamprou et al [18] consider two robots of different speeds. Regarding evacuation with more than two robots, Czyzowicz et al [13] study the setting with three robots, one of which may be faulty. Czyzowicz et al focus on evacuating a single robot, the "queen", that is supported by up to three [14] or more [8] "servants".…”

Section: Related Workmentioning

confidence: 99%

Evacuating Two Robots from a Disk: A Second Cut

Disser

Schmitt

2019

Structural Information and Communication Complexity

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We present an improved algorithm for the problem of evacuating two robots from the unit disk via an unknown exit on the boundary. Robots start at the center of the disk, move at unit speed, and can only communicate locally. Our algorithm improves previous results by Brandt et al. [CIAC'17] by introducing a second detour through the interior of the disk. This allows for an improved evacuation time of 5.6234. The best known lower bound of 5.255 was shown by Czyzowicz et al. [CIAC'15].

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“…The two types of faults considered are crash fault and byzantine fault. The type of crash fault considered in [6,11] does not detect the target when it passes through or does not communicate when it finds the target. The robots with byzantine faults in [6,9] even lie about the position of the target.…”

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confidence: 99%

“…The type of crash fault considered in [6,11] does not detect the target when it passes through or does not communicate when it finds the target. The robots with byzantine faults in [6,9] even lie about the position of the target. Czyzowicz et al [6] focused on minimizing the evacuation time for the latest non-faulty robot.…”

mentioning

confidence: 99%

“…They achieved a lower bound of 5.188 and upper bound 6.309 for three robots out of which at most one is susceptible to crash fault with wireless communication. We initiate the study on a type of crash fault, where the robot stops moving and sending messages altogether (unlike [6]). Instead of abandoning the crashed robot, our objective is to chauffeur it to the exit in the least time.…”

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confidence: 99%

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Chauffeuring a Crashed Robot from a Disk

Pattanayak

Ramesh

Mandal

2019

Algorithms for Sensor Systems

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Evacuation of robots from a disk has attained a lot of attention recently. We visit the problem from the perspective of fault-tolerance. We consider two robots trying to evacuate from a disk via a single hidden exit on the perimeter of the disk. The robots communicate wirelessly. The robots are susceptible to crash faults after which they stop moving and communicating. We design the algorithms for tolerating one fault. The objective is to minimize the worst-case time required to evacuate both the robots from the disk. When the non-faulty robot chauffeurs the crashed robot, it takes α ≥ 1 amount of time to travel unit distance. With this, we also provide a lower bound for the evacuation time. Further, we evaluate the worst-case of the algorithms for different values of α and the crash time.

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Evacuation from a Disc in the Presence of a Faulty Robot

Cited by 36 publications

References 23 publications

Evacuating equilateral triangles and squares in the face-to-face model

Evacuating equilateral triangles and squares in the face-to-face model

Evacuating Two Robots from a Disk: A Second Cut

Chauffeuring a Crashed Robot from a Disk

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