Simple agents learn to find their way: An introduction on mapping polygons

Chalopin, Jérémie; Das, Shantanu; Disser, Yann; Mihaľák, Matúš; Widmayer, Peter

doi:10.1016/j.dam.2013.01.006

Cited by 4 publications

(5 citation statements)

References 37 publications

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“…The agents start from their initial configuration and may gain some knowledge on the topology of the graph only as a result of its path traversals. The task to be performed varies and may include exploration [2,12,20,26], map construction [10,14,18], gathering [13,19,32,40] or leader election [5,6,28]. In this work we focus on the task of capturing a fast fugitive hiding in the graph.…”

Section: Introductionmentioning

confidence: 99%

Distributed graph searching with a sense of direction

2014

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In this work we consider the edge searching problem for vertex-weighted graphs with arbitrarily fast and invisible fugitive. The weight function ω provides for each vertex v the minimum number of searchers required to guard v, i.e., the fugitive may not pass through v without being detected only if at least ω(v) searchers are present at v. This problem is a generalization of the classical edge searching problem, in which one has ω ≡ 1. We assume that with a graph G to be searched, there is associated a partition (V 1 , . . . , V t ) of its vertex set such that edges are allowed only within each V i and between two consecutive V i 's. We provide an algorithm for distributed monotone connected edge searching of such graphs, where the searchers are initially placed on an arbitrary vertex of G and have no a priori knowledge on G, but they have a sense of direction that lets them recognize whether an edge incident to already explored vertex in V i leads to a vertex in one of V i−1 , V i or V i+1 . Starting from any vertex the algorithm uses at most 3·max i=1,...,t ω(V i )+1 searchers, where ω(V i ) = v∈V i ω(v). We also prove that this algorithm is best possible up to a small additive constant, that is, each distributed searching algorithm in worst case must use 3 · max i=1,...,t ω(V i ) − 1 searchers for some graphs.

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Section: Introductionmentioning

confidence: 99%

Distributed graph searching with a sense of direction

2014

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“…Recall that a sub-routine of our Meeting algorithms consists in drawing a map of the polygon. A related problem is that of constructing the visibility graph of a polygon by mobile robots [5,6,7]. Here the effort has been focused on finding minimal assumptions on the robots' power that allow them to solve the problem.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Meeting in a polygon by anonymous oblivious robots

et al. 2019

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The Meeting problem for k ≥ 2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P , according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of P , we minimize the number of searchers k for which the Meeting problem is solvable. Specifically, if P has a rotational symmetry of order σ (where σ = 1 corresponds to no rotational symmetry), we prove that k = σ +1 searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with k = 2 searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations (provided that the coordinates of the polygon's vertices are algebraic real numbers in some global coordinate system), and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.

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“…However, their model is significantly different from [18]. Another problem related to our map construction problem is that of constructing the visibility graph of a polygon by mobile robots [4][5][6]14].…”

Section: Related Workmentioning

confidence: 99%

Positional Encoding by Robots with Non-rigid Movements

Bose

Adhikary

Kundu

et al. 2019

Structural Information and Communication Complexity

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Consider a set of autonomous computational entities, called robots, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant δ > 0, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than δ amount. This model is known in literature as non-rigid movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having O(1) bits of persistent memory and ability to make circular moves.

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Simple agents learn to find their way: An introduction on mapping polygons

Abstract: International audienceSimple agents learn to find their way: An introduction on mapping polygon

Cited by 4 publications

References 37 publications

Distributed graph searching with a sense of direction

Distributed graph searching with a sense of direction

Meeting in a polygon by anonymous oblivious robots

Positional Encoding by Robots with Non-rigid Movements

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