Wireless Autonomous Robot Evacuation from Equilateral Triangles and Squares

Czyzowicz, Jurek; Kranakis, Evangelos; Kriz̧anc, Danny; Narayanan, Lata; Opatrný, Jaroslav; Shende, Sunil

doi:10.1007/978-3-319-19662-6_13

Cited by 46 publications

(48 citation statements)

References 13 publications

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“…The agents move to explore k segments on all three sides, subsequently entering the interior of the triangle to form a connected network in order to communicate the results to the other agents, after which they either move to the exit or they all explore the remaining segment. In the second strategy, called Explore 1 Side before Connecting (X1C) only one of the sides of the triangle is partitioned into multiple segments, each to be explored by an 2.3367 see [9] 2.0887 see [9] 1.98157 see [9] 1.78867 see [15] 1.66666 see [14] 1.61050 see [14] agent. At the end of the exploration of the edge, two of the agents explore the remaining two sides of the triangle, while the other agents move inside to create and maintain connectivity of all agents.…”

Section: Our Resultsmentioning

confidence: 99%

“…Finally we consider in Section 5 the problem of the optimal evacuation of k agents. It was shown in [14] that for any r, regardless of the number of agents, evacuation cannot be done in time less that 1 + √ 3/3; on the other hand, this time can be achieved by 6 agents and r = 1. In this paper we show that for any r > 0, evacuation can achieved in the optimal time of 1 + √ 3/3 if the number of agents is 6 + 2 ( 1 r − 1) .…”

Section: Our Resultsmentioning

confidence: 99%

“…The problem for the face-to-face model was revisited in [12], and the results further improved in [6]. The evacuation of an equilateral triangle with agents in the wireless model was considered in [14], and in the face-to-face communication model in [9]. We should also mention the work on polygons [19], evacuation of circle with faulty agents [12], and the case of multiple exits on a circle [10,25].…”

Section: Related Workmentioning

confidence: 99%

“…To the best of our knowledge, the case of limited range communication of agents in evacuation problems has not been considered yet. Since the evacuation of the equilateral triangle was previously studied for the face-toface model [9] and the wireless model [14], it will allow us to evaluate the impact of the limited transmission range on the evacuation algorithms. When there are three or more agents, then an agent can act as a relay between two other agents, thereby increasing the effective communication range of the agents.…”

Section: Introductionmentioning

confidence: 99%

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Evacuation of Equilateral Triangles by Mobile Agents of Limited Communication Range

Bagheri

Narayanan

Opatrný

2019

Algorithms for Sensor Systems

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We consider the problem of evacuating k ≥ 2 mobile agents from a unit-sided equilateral triangle through an exit located at an unknown location on the perimeter of the triangle. The agents are initially located at the centroid of the triangle and they can communicate with other agents at distance at most r with 0 ≤ r ≤ 1. An agent can move at speed at most one, and finds the exit only when it reaches the point where the exit is located. The agents can collaborate in the search for the exit. The goal of the evacuation problem is to minimize the evacuation time, defined as the worst-case time for all the agents to reach the exit.We propose and analyze several algorithms for the problem of evacuation by k ≥ 2 agents; our results indicate that the best strategy to be used varies depending on the values of r and k. For two agents, we give three algorithms, each of which achieves the best performance for different sub-ranges of r in the range 0 ≤ r ≤ 1. We also show a lower bound on the evacuation time of two agents for any r < 0.336. For k > 2 agents, we study three strategies for evacuation: in the first strategy, called X3C, agents explore all three sides of the triangle before connecting to exchange information; in the second strategy, called X1C, agents explore a single side of the triangle before connecting; in the third strategy, called CXP, the agents travel to the perimeter to locations in which they are connected, and explore it while always staying connected. For 3 or 4 agents, we show that X3C works better than X1C for small values of r, while X1C works better for larger values of r. Finally, we show that for any r, evacuation of k = 6 + 2 ( 1 r − 1) agents can be done using the CXP strategy in time 1 + √ 3/3, which is optimal in terms of time, and asymptotically optimal in terms of the number of agents.

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Section: Our Resultsmentioning

confidence: 99%

Section: Our Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evacuation of Equilateral Triangles by Mobile Agents of Limited Communication Range

Bagheri

Narayanan

Opatrný

2019

Algorithms for Sensor Systems

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“…[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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Priority Evacuation from a Disk Using Mobile Robots

Czyzowicz

Georgiou

Killick

et al. 2018

Lecture Notes in Computer Science

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We introduce and study a new search-type problem with (n + 1)-robots on a disk. The searchers (robots) all start from the center of the disk, have unit speed, and can communicate wirelessly. The goal is for a distinguished robot (the queen) to reach and evacuate from an exit that is hidden on the perimeter of the disk in as little time as possible. The remaining n robots (servants) are there to facilitate the queen's objective and are not required to reach the hidden exit. We provide upper and lower bounds for the time required to evacuate the queen from a unit disk. Namely, we propose an algorithm specifying the trajectories of the robots which guarantees evacuation of the queen in time always better than 2 + 4( √ 2 − 1) π n for n ≥ 4 servants. We also demonstrate that for n ≥ 4 servants the queen cannot be evacuated in time less than 2 + π n + 2 n 2 .

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Wireless Autonomous Robot Evacuation from Equilateral Triangles and Squares

Cited by 46 publications

References 13 publications

Evacuation of Equilateral Triangles by Mobile Agents of Limited Communication Range

Evacuation of Equilateral Triangles by Mobile Agents of Limited Communication Range

Linear Search by a Pair of Distinct-Speed Robots

Priority Evacuation from a Disk Using Mobile Robots

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