Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots

Bampas, Evangelos; Das, Shantanu; Dereniowski, Dariusz; Karousatou, Christina

doi:10.1007/978-3-319-72751-6_1

Cited by 6 publications

(7 citation statements)

References 16 publications

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“…⇐ We now show that if Φ is not satisfiable then every solution to MinDiam with arbitrary stops is of size greater than or equal to 2b + 4 3 b = 10 3 b. As in the case of node stops, we note that if in a configuration C there are two agents i, j which move away from their starting positions p i , p j by a distance of at most δ := b 3 , then they must have a distance of at least 10 3 b.…”

Section: Additive Approximation and Conclusionmentioning

confidence: 89%

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Near-gathering of energy-constrained mobile agents

Bärtschi

Bampas

Chalopin

et al. 2021

Theoretical Computer Science

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We study the task of gathering k energy-constrained mobile agents in an undirected edgeweighted graph. Each agent is initially placed on an arbitrary node and has a limited amount of energy, which constrains the distance it can move. Since this may render gathering at a single point impossible, we study three variants of near-gathering: The goal is to move the agents into a configuration that minimizes either (i) the radius of a ball containing all agents, (ii) the maximum distance between any two agents, or (iii) the average distance between the agents. We prove that (i) is polynomial-time solvable, (ii) has a polynomial-time 2-approximation with a matching NP-hardness lower bound, while (iii) admits a polynomial-time 2(1 − 1 k)-approximation, but no FPTAS, unless P = NP. We extend some of our results to additive approximation.

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Section: Additive Approximation and Conclusionmentioning

confidence: 89%

“…The problem of delivering packages by multiple agents having energy constraints was studied in [9,10,7,8]. All of these problems were shown to be NP-hard for general graphs even if the agents are allowed to exchange energy when they meet [14,4].…”

Section: Definition 1 (Near-gathering)mentioning

confidence: 99%

Near-gathering of energy-constrained mobile agents

Bärtschi

Bampas

Chalopin

et al. 2021

Theoretical Computer Science

Self Cite

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“…Czyzowicz et al [19] recently showed that the problems of collaborative delivery, broadcast and convergecast remain NP-hard for general graphs even if the agents are allowed to exchange energy when they meet. Further results on collective delivery with energy exchange showed that the problem remains hard even when B is a small constant [20].…”

Section: Related Workmentioning

confidence: 99%

Collaborative delivery on a fixed path with homogeneous energy-constrained agents

Chalopin

Das

Disser

et al. 2021

Theoretical Computer Science

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We consider the problem of collectively delivering a package from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent starts from some vertex of the graph; it can move along the edges of the graph and can can pick up the package from a vertex and drop it in another vertex during the course of its movement. However, each agent has limited energy budget allowing it to traverse a path of bounded length B; thus, multiple agents need to collaborate to move the package to its destination. Given the positions of the agents in the graph and their energy budgets, the problem of finding a feasible movement schedule is called the Collaborative Delivery problem and has been studied before.One of the open questions from previous results is what happens when the delivery must follow a fixed path given in advance. Although this special constraint reduces the search space for feasible solutions, we show that the problem of finding a feasible schedule remains NP hard (as the original problem). We consider the optimization version of the problem that asks for the optimal energy budget B per agent which allows for a feasible delivery schedule, given the initial positions of the agents. We show the existence of better approximations for the fixed-path version of the problem (at least for the restricted case of a single pickup per agent), compared to the known results for the general version of the problem.We provide polynomial time approximation algorithms for both directed and $ This work was partially supported by the ANR project ANCOR (anr-14-CE36-0002-01).

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“…The case of robots that can share energy has been recently studied for the tasks of data communication, [6,12,13,14,25]. In this research the robots are distributed in different places of the network, each robot initially possessing some amount of energy, possibly distinct for different robots.…”

Section: Related Workmentioning

confidence: 99%

“…It is interesting to investigate what tasks might be made possible with this new capability, given the same initial amounts of energies. In [6,12,13,14,25], researchers have studied the problems of data delivery, broadcast, and convergecast by energy-sharing mobile agents.…”

Section: Introductionmentioning

confidence: 99%

Graph Exploration by Energy-Sharing Mobile Agents

Czyzowicz

Dobrev

Killick

et al. 2021

Preprint

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We consider the problem of collective exploration of a known n-node edge-weighted graph by k mobile agents that have limited energy but are capable of energy transfers. The agents are initially placed at an arbitrary subset of nodes in the graph, and each agent has an initial, possibly different, amount of energy. The goal of the exploration problem is for every edge in the graph to be traversed by at least one agent. The amount of energy used by an agent to travel distance x is proportional to x. In our model, the agents can share energy when co-located: when two agents meet, one can transfer part of its energy to the other.For an n-node path, we give an O(n+k) time algorithm that either finds an exploration strategy, or reports that one does not exist. For an n-node tree with leaves, we give an O(n+ k 2 ) algorithm that finds an exploration strategy if one exists. Finally, for the general graph case, we show that the problem of deciding if exploration is possible by energy-sharing agents is NP-hard, even for 3-regular graphs. In addition, we show that it is always possible to find an exploration strategy if the total energy of the agents is at least twice the total weight of the edges; moreover, this is asymptotically optimal.

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Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots

Cited by 6 publications

References 16 publications

Near-gathering of energy-constrained mobile agents

Near-gathering of energy-constrained mobile agents

Collaborative delivery on a fixed path with homogeneous energy-constrained agents

Graph Exploration by Energy-Sharing Mobile Agents

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