Evacuating two robots from multiple unknown exits in a circle

Czyzowicz, Jurek; Dobrev, Štefan; Georgiou, Konstantinos; Kranakis, Evangelos; MacQuarrie, Fraser

doi:10.1016/j.tcs.2016.11.019

Cited by 19 publications

(14 citation statements)

References 13 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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“…Since the introduction of 2 EVAC F 2F in [16], a number of variants emerged, focusing on different geometric domains, different number of robots and robots' specifications, different communication models etc. Examples include evacuation from the disk with more than 1 exits in the wireless model [15], evacuation of a group of robots on a line [13] (generalization of the celebrated Cow-Path problem [6]), evacuation in the presence of faulty robots in a line [20] and in a disk [17], evacuation with advice [29] while more recently evacuation with combinatorial requirements on the robots that need to evacuate, e.g. [27,28,18,19].…”

Section: Related Workmentioning

confidence: 99%

Average Case - Worst Case Tradeoffs for Evacuating 2 Robots from the Disk in the Face-to-Face Model

Chuangpishit

Georgiou

Sharma

2019

Algorithms for Sensor Systems

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The problem of evacuating two robots from the disk in the face-to-face model was first introduced in [16], and extensively studied (along with many variations) ever since with respect to worst case analysis. We initiate the study of the same problem with respect to average case analysis, which is also equivalent to designing randomized algorithms for the problem. First we observe that algorithm B2 of [16] with worst case cost Wrs (B2) := 5.73906 has average case cost Avg (B2) := 5.1172. Then we verify that none of the algorithms that induced worst case cost improvements in subsequent publications has better average case cost, hence concluding that our problem requires the invention of new algorithms. Then, we observe that a remarkable simple algorithm, B1, has very small average case cost Avg (B1) := 1 + π, but very high worst case cost Wrs (B1) := 1 + 2π. Motivated by the above, we introduce constrained optimization problem 2 EVAC w F 2F , in which one is trying to minimize the average case cost of the evacuation algorithm given that the worst case cost does not exceed w. The problem is of special interest with respect to practical applications, since a common objective in search-and-rescue operations is to minimize the average completion time, given that a certain worst case threshold is not exceeded, e.g. for safety or limited energy reasons. Our main contribution is the design and analysis of families of new evacuation parameterized algorithms A (p) which can solve 2 EVAC w F 2F , for every w ∈ [Wrs (B1) , Wrs (B2)]. In particular, by letting parameter(s) p vary, we obtain parametric curve (Avg (A (p)) , Wrs (A (p))) that induces a continuous and strictly decreasing function in the mean-worst case space, and whose endpoints are (Avg (B1) , Wrs (B1)) , (Avg (B2) , Wrs (B2)). Notably, the worst case analysis of the problem, since it's introduction, has been relying on technical numerical, computerassisted, calculations, following tedious robots trajectories' analysis. Part of our contribution is a novel systematic procedure, which, given any evacuation algorithm, can derive it's worst and average case performance in a clean and unified way.

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“…Most results were obtained for evacuation from the disk with wireless communication, i.e., for robots that can exchange information at all times. Czyzowicz et al [20] and Pattanayak et al [11] consider evacuation with multiple exits and known positions of the exists relative to each other. Lamprou et al [18] consider two robots of different speeds.…”

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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Evacuating two robots from multiple unknown exits in a circle

Cited by 19 publications

References 13 publications

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

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

Average Case - Worst Case Tradeoffs for Evacuating 2 Robots from the Disk in the Face-to-Face Model

Evacuating Two Robots from a Disk: A Second Cut

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