Evacuating Robots via Unknown Exit in a Disk

Czyzowicz, Jurek; Gąsieniec, Leszek; Gorry, Thomas; Kranakis, Evangelos; Martin, Russell; Pająk, Dominik

doi:10.1007/978-3-662-45174-8_9

Cited by 57 publications

(98 citation statements)

References 18 publications

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“…The upper bound for evacuation in the wireless communication model is 1 + 2π/3 + 3. This is the worst-case evacuation time of the algorithm proposed by Czyzowicz et al [5]. In this paper, we also present evacuation strategies which determine the upper bound with chauffeuring.…”

Section: Upper Bound For Wireless Communicationmentioning

confidence: 96%

“…The lower bound for wireless communication model without faults is 1+2π/3+ 3 ≈ 4.826 [5]. Hence, the lower bound is applicable to the crash fault model if the crash time w ≥ 1 + 2π/3 + 3.…”

Section: Lower Bounds For Wireless Communicationmentioning

confidence: 96%

“…Otherwise, if the unexplored part is separated into multiple arcs, then the distance between two farthest endpoints of the two arcs are at least separated by a distance which is greater than the unexplored part u ≤ π. A detailed proof is available in [5].…”

Section: Lemma 1 (Lemma 5 From [5]mentioning

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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Section: Upper Bound For Wireless Communicationmentioning

confidence: 96%

Section: Lower Bounds For Wireless Communicationmentioning

confidence: 96%

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Chauffeuring a Crashed Robot from a Disk

Pattanayak

Ramesh

Mandal

2019

Algorithms for Sensor Systems

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“…Sometimes the searching robot is not looking for an individual target point, attempting rather to evacuate being lost in an unknown environment or determine its position within a known map (e.g. [18,24]). Several of these research papers offer exciting challenges of combinatorial or algorithmic nature (see [26]).…”

Section: Related Workmentioning

confidence: 99%

“…[13,14,17,18,21]). For other problems considering robots with distinct speeds (e.g., the patrolling problem studied in [16,19,33]), only partial results were obtained.…”

Section: Related Workmentioning

confidence: 99%

Linear Search by a Pair of Distinct-Speed Robots

Bampas¹,

Czyzowicz²,

Gąsieniec³

et al. 2016

Structural Information and Communication Complexity

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Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look 123Algorithmica for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with a robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (in: Italiano, Margaria-Steffen, Pokorný, Quisquater, Wattenhofer (eds) Current trends in theory and practice of computer science, SOFSEM, 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In the wireless communication model, a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. For this model, we design a strategy which is optimal whenever the faster robot is at most √ 17 + 4 ≈ 8.123 times faster than the slower one. We also prove that otherwise the wireless communication offers no advantage over communication by meeting.

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Evacuation from various types of finite two‐dimensional square grid fields by a metamorphic robotic system

Nakamura

Kamei

Yamauchi

2021

Concurrency and Computation

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Summary A metamorphic robotic system (MRS) is composed of anonymous, memoryless, and autonomous modules that execute an identical distributed algorithm to move while keeping the connectivity of the modules. For an MRS, the number of modules required to solve a given task is an important complexity measure. Here, we consider evacuation from a finite two‐dimensional square grid field by an MRS. This study aims to establish the minimum number of modules required to solve the evacuation problem under several conditions. We consider a rectangular field surrounded by walls with at least one exit. Our results show that two modules are necessary and sufficient for evacuation from any rectangular field if equipped with a global compass, which provides the modules with a common sense of direction. After that, we focus on the case of modules without a global compass and show that four (resp. seven) modules are necessary and sufficient for restricted (resp. any) initial shapes of an MRS. We also show that two modules are sufficient when an MRS is touching a wall in an initial configuration. Then, we clarify the condition to stop an MRS after evacuation of a rectangular field. Finally, we extend these results to mazes and convex fields.

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Evacuating Robots via Unknown Exit in a Disk

Cited by 57 publications

References 18 publications

Chauffeuring a Crashed Robot from a Disk

Chauffeuring a Crashed Robot from a Disk

Linear Search by a Pair of Distinct-Speed Robots

Evacuation from various types of finite two‐dimensional square grid fields by a metamorphic robotic system

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