Evacuating two robots from multiple unknown exits in a circle

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

doi:10.1145/2833312.2833318

Cited by 23 publications

(16 citation statements)

References 19 publications

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“…Variations pertaining to the searcher's speeds appeared in [36,37] (immobile agents), in [44] (speed bounds) and in [26] (terrain dependent speeds). Search for multiple exits was considered in [28,50], while variation of searching with advice appeared in [40]. Some variations of the objective include the so-called priority evacuation problem [23,30] and its generalization of weighted searchers [39].…”

Section: Related Workmentioning

confidence: 99%

Evacuating from ell_p Unit Disks in the Wireless Model

Georgiou¹,

Leizerovich²,

Lucier³

et al. 2021

Preprint

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The search-type problem of evacuating 2 robots in the wireless model from the (Euclidean) unit disk was first introduced and studied by Czyzowicz et al. [DISC'2014]. Since then, the problem has seen a long list of follow-up results pertaining to variations as well as to upper and lower bound improvements. All established results in the area study this 2-dimensional search-type problem in the Euclidean metric space where the search space, i.e. the unit disk, enjoys significant (metric) symmetries. We initiate and study the problem of evacuating 2 robots in the wireless model from p unit disks, p ∈ [1, ∞), where in particular robots' moves are measured in the underlying metric space. To the best of our knowledge, this is the first study of a search-type problem with mobile agents in more general metric spaces. The problem is particularly challenging since even the circumference of the p unit disks have been the subject of technical studies. In our main result, and after identifying and utilizing the very few symmetries of p unit disks, we design optimal evacuation algorithms that vary with p. Our main technical contributions are two-fold. First, in our upper bound results, we provide (nearly) closed formulae for the worst case cost of our algorithms. Second, and most importantly, our lower bounds' arguments reduce to a novel observation in convex geometry which analyzes trade-offs between arc and chord lengths of p unit disks as the endpoints of the arcs (chords) change position around the perimeter of the disk, which we believe is interesting in its own right. Part of our argument pertaining to the latter property relies on a computer assisted numerical verification that can be done for nonextreme values of p.

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Section: Related Workmentioning

confidence: 99%

Evacuating from ell_p Unit Disks in the Wireless Model

Georgiou¹,

Leizerovich²,

Lucier³

et al. 2021

Preprint

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“…Since the inception of 2 EVAC F2F in [1], numerous search and evacuation-type variants have emerged that studied different robot specs and/or number of searchers, different communication models, and different domains. Some notable examples include search and/or evacuation in the disk with more than 1 exits [29,30], in triangles [31,32], on multiple rays [33], in graphs [34,35], on a line with at least two robots [36,37] (generalizing the seminal result of [38]), with faulty robots [39][40][41] or with probabilistically faulty robots [42], with advice (information) [43], with priority specification on the searchers [44,45], with immobile agents [46,47], with time/energy trade-off requirements [48,49], with speed bounds [50], and with terrain dependent speeds [51], just to name some. The interested reader may also see the recent survey [52] that elaborates more on some selected topics.…”

Section: Related Workmentioning

confidence: 99%

A Multi-Objective Optimization Problem on Evacuating 2 Robots from the Disk in the Face-to-Face Model; Trade-Offs between Worst-Case and Average-Case Analysis

2020

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The problem of evacuating two robots from the disk in the face-to-face model was first introduced by Czyzowicz et al. [DISC’2014], and has been 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. In particular, we introduce constrained optimization problem 2EvacF2F, 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 which can solve 2EvacF2F, for every w for which the problem is feasible. Notably, the worst-case analysis of the problem, since its introduction, has been relying on technical numerical, computer-assisted calculations, following tedious robot trajectory analysis. Part of our contribution is a novel systematic procedure, which given any evacuation algorithm, can derive its 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 23 publications

References 19 publications

Evacuating from ell_p Unit Disks in the Wireless Model

Evacuating from ell_p Unit Disks in the Wireless Model

A Multi-Objective Optimization Problem on Evacuating 2 Robots from the Disk in the Face-to-Face Model; Trade-Offs between Worst-Case and Average-Case Analysis

Evacuating Two Robots from a Disk: A Second Cut

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