How many oblivious robots can explore a line

Flocchini, Paola; Ilcinkas, David; Pełc, Andrzej; Santoro, Nicola

doi:10.1016/j.ipl.2011.07.018

Cited by 29 publications

(20 citation statements)

References 22 publications

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“…In general, the more complex setting of using multiple identical agents has received much less attention. Exploration by deterministic multiple agents was studied in, e.g., [31,32]. To obtain better results when using several identical deterministic agents, one must assume that the agents are either centrally coordinated or that they have some means of communication (either explicitly, or implicitly, by being able to detect the presence of nearby agents).…”

Section: Related Workmentioning

confidence: 99%

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The ANTS problem

Feinerman

Korman

2016

Distrib. Comput.

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We introduce the Ants Nearby Treasure Search (ANTS) problem, which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k probabilistic agents, initially placed at a central location, collectively search for a treasure on the two-dimensional grid. The treasure is placed at a target location by an adversary and the agents' goal is to find it as fast as possible as a function of both k and D, where D is the (unknown) distance between the central location and the target. We concentrate on the case in which agents cannot communicate while searching. It is straightforward to see that the time until at least one agent finds the target is at least $\Omega$(D + D 2 /k), even for very sophisticated agents, with unrestricted memory. Our algorithmic analysis aims at establishing connections between the time complexity and the initial knowledge held by agents (e.g., regarding their total number k), as they commence the search. We provide a range of both upper and lower bounds for the initial knowledge required for obtaining fast running time. For example, we prove that log log k + $\Theta$(1) bits of initial information are both necessary and sufficient to obtain asymptotically optimal running time, i.e., O(D +D 2 /k). We also we prove that for every 0 \textless{} \textless{} 1, running in time O(log 1-- k $\times$(D +D 2 /k)) requires that agents have the capacity for storing $\Omega$(log k) different states as they leave the nest to start the search. To the best of our knowledge, the lower bounds presented in this paper provide the first non-trivial lower bounds on the memory complexity of probabilistic agents in the context of search problems. We view this paper as a "proof of concept" for a new type of interdisciplinary methodology. To fully demonstrate this methodology, the theoretical tradeoff presented here (or a similar one) should be combined with measurements of the time performance of searching ants.Comment: arXiv admin note: text overlap with arXiv:1205.454

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Section: Related Workmentioning

confidence: 99%

“…In this distributed setting, we are concerned with the speed-up measure (see also, [6,7,31,32]), which aims to capture the impact of using k searchers in comparison to using a single one. Note that the objectives of quickly finding nearby treasures and having significant speed-up may be at conflict.…”

Section: Introductionmentioning

confidence: 99%

The ANTS problem

Feinerman

Korman

2016

Distrib. Comput.

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“…The ANTS problem generalizes the cow-path problem, as it considers multiple identical agents instead of a single agent (a cow in their terminology). Indeed, in this distributed setting, we are concerned with the speed-up measure (see also, [8,9,27,29]), which aims to capture the impact of using k searchers in comparison to using a single one. Note that the objectives of quickly finding nearby treasures and having significant speed-up may be at conflict.…”

Section: Background and Motivationmentioning

confidence: 99%

Collaborative search on the plane without communication

Feinerman

Korman

Lotker

et al. 2012

Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing

103

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We generalize the classical cow-path problem [7, 14, 38, 39] into a question that is relevant for collective foraging in animal groups. Specifically, we consider a setting in which k identical (probabilistic) agents, initially placed at some central location, collectively search for a treasure in the two-dimensional plane. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the distance between the central location and the target. This is biologically motivated by cooperative, central place foraging such as performed by ants around their nest. In this type of search there is a strong preference to locate nearby food sources before those that are further away. Our focus is on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents must be highly dispersed making communication difficult. Furthermore, if agents do not commence the search in synchrony then even initial communication is problematic. This holds, in particular, with respect to the question of whether the agents can communicate and conclude their total number, k. It turns out that the knowledge of k by the individual agents is crucial for performance. Indeed, it is a straightforward observation that the time required for finding the treasure is $\Omega$(D + D 2 /k), and we show in this paper that this bound can be matched if the agents have knowledge of k up to some constant approximation. We present an almost tight bound for the competitive penalty that must be paid, in the running time, if agents have no information about k. Specifically, on the negative side, we show that in such a case, there is no algorithm whose competitiveness is O(log k). On the other hand, we show that for every constant $\epsilon \textgreater{} 0$, there exists a rather simple uniform search algorithm which is $O( \log^{1+\epsilon} k)$-competitive. In addition, we give a lower bound for the setting in which agents are given some estimation of k. As a special case, this lower bound implies that for any constant $\epsilon \textgreater{} 0$, if each agent is given a (one-sided) $k^\epsilon$-approximation to k, then the competitiveness is $\Omega$(log k). Informally, our results imply that the agents can potentially perform well without any knowledge of their total number k, however, to further improve, they must be given a relatively good approximation of k. Finally, we propose a uniform algorithm that is both efficient and extremely simple suggesting its relevance for actual biological scenarios

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“…In [9], the authors present a gathering algorithm for myopic agents in the plane requiring that they agree on a common coordinate system. In the discrete model, gathering and exploration are the two main problems that have been investigated so far e.g., [11], [12], [14], [15] for the gathering problem and [3], [5], [6], [16], [7] for the exploration problem.…”

Section: A Related Workmentioning

confidence: 99%

“…The same authors characterize in [7] the number of agents capable of exploring the special case of tree reduced to a line. In [5], it is proved that no deterministic exploration is possible on a ring when the number of agents k divides the number of nodes n. In the same paper, the authors propose a deterministic algorithm that solves the problem using at least 17 agents, provided that n and k are co-prime.…”

Section: A Related Workmentioning

confidence: 99%

Ring Exploration by Oblivious Agents with Local Vision

Datta

Lamani

Larmore

et al. 2013

2013 IEEE 33rd International Conference on Distributed Computing Systems

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International audienceThe problem of exploring a discrete environment by identical oblivious asynchronous agents (or robots) devoid of direct means of communication has been well investigated so far. The (terminating) exploration requires that starting from a configuration where no two agents occupy the same node, every node needs to be visited by at least one agent, with the additional constraint that all agents eventually stop moving. Agents have sensors that allow them to see their environment and move accordingly. The previous works on this problem assume agents having an unlimited visibility, that is, they can sense the agents on every node of the ring, whatever the ring size. In this paper, we address deterministic exploration in an anonymous, unoriented ring using oblivious, and myopic agents. By myopic, we mean that their visibility is limited in terms of sensing distance. We consider the strongest possible myopia that is, an agent can only sense agents located at its own and at its immediate neighboring nodes. Our contribution is threefold. We first prove that within such settings, no deterministic exploration is possible in the semi-synchronous model. The result is also valid for the (fully) asynchronous model and holds for any k < n where k is the number of agents and n is the number of nodes in the ring. Next, we address the synchronous model and show that no deterministic exploration protocol solves the problem with less than five agents when n > 6. Finally, we provide optimal (in terms of number of agents) deterministic algorithms in the fully synchronous model for both cases 2 < n < 7 and n > 6

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How many oblivious robots can explore a line

Cited by 29 publications

References 22 publications

The ANTS problem

The ANTS problem

Collaborative search on the plane without communication

Ring Exploration by Oblivious Agents with Local Vision

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