Collaborative Exploration of Trees by Energy-Constrained Mobile Robots

Das, Shantanu; Dereniowski, Dariusz; Karousatou, Christina

doi:10.1007/s00224-017-9816-3

Cited by 18 publications

(5 citation statements)

References 18 publications

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“…In [12] it is shown that deciding whether the agents can deliver the data is (weakly) NP-complete. Additional research under various conditions and topological assumptions can be found in [4] which studies the game-theoretic task of selecting mobile agents to deliver multiple items on a network and optimizing or approximating the total energy consumption over all selected agents, in [2,5,7] which study data delivery and combine energy and time efficiency, and in [18,19] which are concerned with collaborative exploration in various topologies.…”

Section: Related Workmentioning

confidence: 99%

Message Delivery in the Plane by Robots with Different Speeds

Coleman¹,

Kranakis²,

Kriz̧anc³

et al. 2021

Preprint

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We study a fundamental cooperative message-delivery problem on the plane. Assume n robots which can move in any direction, are placed arbitrarily on the plane. Robots each have their own maximum speed and can communicate with each other face-to-face (i.e., when they are at the same location at the same time). There are also two designated points on the plane, S (the source) and D (the destination). The robots are required to transmit the message from the source to the destination as quickly as possible by face-to-face message passing. We consider both the offline setting where all information (the locations and maximum speeds of the robots) are known in advance and the online setting where each robot knows only its own position and speed along with the positions of S and D. In the offline case, we discover an important connection between the problem for two-robot systems and the well-known Apollonius circle which we employ to design an optimal algorithm. We also propose a √ 2 approximation algorithm for systems with any number of robots. In the online setting, we provide an algorithm with competitive ratio 1 7 5 + 4 √ 2 for two-robot systems and show that the same algorithm has a competitive ratio less than 2 for systems with any number of robots. We also show these results are tight for the given algorithm. Finally, we give two lower bounds (employing different arguments) on the competitive ratio of any online algorithm, one of 1.0391 and the other of 1.0405.

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Section: Related Workmentioning

confidence: 99%

Message Delivery in the Plane by Robots with Different Speeds

Coleman¹,

Kranakis²,

Kriz̧anc³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Additional research under various conditions and topological assumptions can be found in [2] which studies the game-theoretic task of selecting mobile agents to deliver multiple items on a network and optimizing or approximating the total energy consumption over all selected agents, in [3] which studies data delivery and combines energy and time efficiency, and in [11,12] which is concerned with collaborative exploration in various topologies.…”

Section: Related Workmentioning

confidence: 99%

The Pony Express Communication Problem

Coleman¹,

Kranakis²,

Kriz̧anc³

et al. 2021

Preprint

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We introduce a new problem which we call the Pony Express problem. n robots with differing speeds are situated over some domain. A message is placed at some commonly known point. Robots can acquire the message either by visiting its initial position, or by encountering another robot that has already acquired it. The robots must collaborate to deliver the message to a given destination 6 .The objective is to deliver the message in minimum time. In this paper we study the Pony Express problem on the line where n robots are arbitrarily deployed along a finite segment. We are interested in both offline centralized and online distributed algorithms. In the online case, we assume the robots have limited knowledge of the initial configuration. In particular, the robots do not know the initial positions and speeds of the other robots nor even their own position and speed. They do, however, know the direction on the line in which to find the message and have the ability to compare speeds when they meet. First, we study the Pony Express problem where the message is initially placed at one endpoint (labeled 0) of a segment and must be delivered to the other endpoint (labeled 1). We provide an O(n log n) running time offline algorithm as well as an optimal (competitive ratio 1) online algorithm. Then we study the Half-Broadcast problem where the message is at the center (at 0) and must be delivered to either one of the endpoints of the segment [−1, +1]. We provide an offline algorithm running in O(n 2 log n) time and we provide an online algorithm that attains a competitive ratio of 3 2 which we show is the best possible. Finally, we study the Broadcast problem where the message is at the center (at 0) and must be delivered to both endpoints of the segment [−1, +1]. Here we give an FPTAS in the offline case and an online algorithm that attains a competitive ratio of 9 5 , which we show is tight.

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“…The robots may be operating on continuous space or graph-like environments. The most fundamental tasks in graphs are Gathering [3, 6, 7, 9, 12-16, 21, 22, 24, 28, 29] and Exploration [4,5,8,10,11,23,27]. A relatively new problem which has attracted a lot of interest recently is Dispersion, introduced by Augustine and Moses Jr. [2].…”

Section: Background and Motivationmentioning

confidence: 99%

Memory Optimal Dispersion by Anonymous Mobile Robots

Das¹,

Bose²,

Sau³

2020

Preprint

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Consider a team of k ≤ n autonomous mobile robots initially placed at a node of an arbitrary graph G with n nodes. The dispersion problem asks for a distributed algorithm that allows the robots to reach a configuration in which each robot is at a distinct node of the graph. If the robots are anonymous, i.e., they do not have any unique identifiers, then the problem is not solvable by any deterministic algorithm. However, the problem can be solved even by anonymous robots if each robot is given access to a fair coin which they can use to generate random bits. In this setting, it is known that the robots require Ω(log ∆) bits of memory to achieve dispersion, where ∆ is the maximum degree of G. On the other hand, the best known memory upper bound is min{∆, max{log ∆, log D}} (D = diameter of G), which can be ω(log ∆), depending on the values of ∆ and D. In this paper, we close this gap by presenting an optimal algorithm requiring O(log ∆) bits of memory.

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Collaborative Exploration of Trees by Energy-Constrained Mobile Robots

Cited by 18 publications

References 18 publications

Message Delivery in the Plane by Robots with Different Speeds

Message Delivery in the Plane by Robots with Different Speeds

The Pony Express Communication Problem

Memory Optimal Dispersion by Anonymous Mobile Robots

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