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

Chuangpishit, Huda; Georgiou, Konstantinos; Sharma, Preeti

doi:10.1007/978-3-030-14094-6_5

Cited by 14 publications

(15 citation statements)

References 35 publications

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“…While most evacuation type problems have focused on the worst-case scenarios, Chuangpishit et al [26] started to explore the algorithms' average case analysis for the problem of evacuating two robots from the disc in the face-to-face model. They found that while worst-case performance of an algorithm improves, the average-case performance worsens for all the previously studied algorithms.…”

Section: Evacuation Problems and Literature Reviewmentioning

confidence: 99%

“…We previously discussed that our intention is to consider the average-case sce- It is also important to mention the results (Figure 3.7b) of a performance analysis [26] recently done for benchmark algorithms B 2 . Figure 3.7b shows a consolidated e ciency-plot for various algorithms as we consider various combinations of and for varying detour-point C as shown in Figure 3.…”

Section: Benchmark Algorithmsmentioning

confidence: 99%

“…Figure 3.7b shows a consolidated e ciency-plot for various algorithms as we consider various combinations of and for varying detour-point C as shown in Figure 3. [26] for families of B…”

Section: Benchmark Algorithmsmentioning

confidence: 99%

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Worst-case & average-case Efficiency trade-offs for search problems

Sharma¹

2021

Preprint

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Evacuation problems fall under the vast area of search theory and operations research. Problems of evacuation of two robots on a unit disc have been studied for an efficient evacuation time. Work done so far has focused on improving the ’worst-case’ evacuation time with deterministic algorithms. We study the ’average-case’ evacuation time (randomized algorithms) while considering the efficiency trade-off between worst-case and average-case costs. Our other contribution is to analyze average-case and worst-case costs for the cowpath problem (another search problem) which helped us to set a parallel method for the evacuation problem.

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Section: Evacuation Problems and Literature Reviewmentioning

confidence: 99%

Section: Benchmark Algorithmsmentioning

confidence: 99%

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Worst-case & average-case Efficiency trade-offs for search problems

Sharma¹

2021

Preprint

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“…The communication model being used may be either wireless [10] or F2F [7,16,19]. Search and evacuation problems with a combinatorial flavour have been recently considered in [12,13] and search-and-fetch problems in [21,22], while [9] studied average-case/worst-case trade-offs for a specific evacuation problem on the disk. The interested reader may also wish to consult a recent survey paper [14] on selected search and evacuation topics.…”

Section: Related Workmentioning

confidence: 99%

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

Czyzowicz

Georgiou

Killick

et al. 2019

Structural Information and Communication Complexity

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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 ≥ 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 ∆. Surprisingly, when ∆ 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 ∆ is linear in d, we give upper bounds on the evacuation time.

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“…A setting similar to ours is presented in the recent works [17,18,21,22,36,12,15] where algorithms are presented in the wireless and non-wireless (or face-to-face) communication models for the evacuation of a team of robots. The "search domain" in [17,18,21,15] is a unit circle (while in [22] the search domain is a triangle or square), however, unlike our search problem, in these papers all the robots are required to evacuate from an unknown exit on the perimeter. Moreover, in none of these papers is there a treasure to be fetched to the exit.…”

Section: Related Workmentioning

confidence: 99%

Search-and-Fetch with 2 Robots on a Disk - Wireless and Face-to-Face Communication Models

Georgiou

Karakostas

Kranakis

2017

Proceedings of the 6th International Conference on Operations Research and Enterprise Systems

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We initiate the study of a new problem on searching and fetching in a distributed environment concerning treasure-evacuation from a unit disk. A treasure and an exit are located at unknown positions on the perimeter of a disk and at known arc distance. A team of two robots start from the center of the disk, and their goal is to fetch the treasure to the exit. At any time the robots can move anywhere they choose on the disk, independently of each other, with the same speed. A robot detects an interesting point (treasure or exit) only if it passes over the exact location of that point. We are interested in designing distributed algorithms that minimize the worst-case treasure-evacuation time, i.e. the time it takes for the treasure to be discovered and brought (fetched) to the exit by any of the robots.The communication protocol between the robots is either wireless, where information is shared at any time, or face-to-face (i.e. non-wireless), where information can be shared only if the robots meet. For both models we obtain upper bounds for fetching the treasure to the exit. Our main technical contribution pertains to the face-to-face model. More specifically, we demonstrate how robots can exchange information without meeting, effectively achieving a highly efficient treasure-evacuation protocol which is minimally affected by the lack of distant communication. Finally, we complement our positive results above by providing a lower bound in the face-to-face model.

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

Cited by 14 publications

References 35 publications

Worst-case & average-case Efficiency trade-offs for search problems

Worst-case & average-case Efficiency trade-offs for search problems

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

Search-and-Fetch with 2 Robots on a Disk - Wireless and Face-to-Face Communication Models

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