Solving the Robots Gathering Problem

Cieliebak, Mark; Flocchini, Paola; Prencipe, Giuseppe; Santoro, Nicola

doi:10.1007/3-540-45061-0_90

Cited by 155 publications

(107 citation statements)

References 14 publications

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“…One of the main difficulties of this problem is to deal with configurations that are totally symmetric, for instance where the robots' positions form a regular 1 n-gon. Recently, an algorithm solving the Gathering Problem has been proposed which uses -among other techniques -the center of equiangularity or biangularity to gather the robots there [4]. Hence, efficient algorithms are needed to find the centers of such configurations.…”

Section: (B)mentioning

confidence: 99%

Efficient Algorithms for Detecting Regular Point Configurations

Anderegg

Cieliebak

Prencipe

2005

Lecture Notes in Computer Science

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Abstract.A set of n points in the plane is in equiangular configuration if there exist a center and an ordering of the points such that the angle of each two adjacent points w.r.t. the center is 360 • n , i.e., if all angles between adjacent points are equal. We show that there is at most one center of equiangularity, and we give a linear time algorithm that decides whether a given point set is in equiangular configuration, and if so, the algorithm outputs the center. A generalization of equiangularity is σ-angularity, where we are given a string σ of n angles and we ask for a center such that the sequence of angles between adjacent points is σ. We show that σ-angular configurations can be detected in time O(n 4 log n).

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Section: (B)mentioning

confidence: 99%

Efficient Algorithms for Detecting Regular Point Configurations

Anderegg

Cieliebak

Prencipe

2005

Lecture Notes in Computer Science

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“…Still there might be an algorithmic transformation to a more "informative/useful" topology (that allows for more powerful global computations) without ever disconnecting the system. Such a transformation is a weaker requirement than, for example, gathering [CFPS03] and may be simpler to obtain.…”

Section: [Fhpmentioning

confidence: 99%

Connectivity preserving network transformers

Michail

Spirakis

2017

Theoretical Computer Science

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The Population Protocol model is a distributed model that concerns systems of very weak computational entities that cannot control the way they interact. The model of Network Constructors is a variant of Population Protocols capable of (algorithmically) constructing abstract networks. Both models are characterized by a fundamental inability to terminate. In this work, we investigate the minimal strengthenings of the latter model that could overcome this inability. Our main conclusion is that initial connectivity of the communication topology combined with the ability of the protocol to transform the communication topology and the ability of a node to detect when its degree is equal to a small constant, plus either a unique leader or the ability of detecting common neighbors, are sufficient to guarantee not only termination but also the maximum computational power that one can hope for in this family of models. The technique of our protocols is to transform any initial connected topology to a less symmetric (that can serve as a large ordered memory) and detectable (that the protocol can determine its successful construction) topology without ever breaking its connectivity during the transformation. The target topology of all of our transformers is the spanning line and we call Terminating Line Transformation the corresponding problem. We first study the case in which there is a pre-elected unique leader and give a time-optimal protocol for Terminating Line Transformation. We then prove that dropping the leader without additional assumptions leads to a strong impossibility result. In an attempt to overcome this, we equip the nodes with the ability to tell, during their pairwise interactions, whether they have at least one neighbor in common. Interestingly, it turns out that this local and realistic mechanism is sufficient to make the problem solvable. In particular, we give a very efficient protocol that solves Terminating Line Transformation when all nodes are initially identical. The latter implies the aforementioned strong characterization: the model, under a few minimal assumptions, computes with termination any symmetric predicate computable by a Turing Machine of space Θ(n 2 ).

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“…Having point-shaped robots, collisions are understood as merges/fusions of robots and interpreted as gathering progress [DKM10]. In [CFPS03] the first gathering algorithm for the ASYN C time model with multiplicity detection (i.e., a robot can detect if other robots are also located at its own position) and global views is provided. Gathering in the local setting was studied in [ASY95].…”

Section: Related Workmentioning

confidence: 99%

Asymptotically Optimal Gathering on a Grid

Cord-Landwehr

Fischer

Jung

et al. 2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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In this paper, we solve the local gathering problem of a swarm of n indistinguishable, pointshaped robots on a two dimensional grid in asymptotically optimal time O(n) in the fully synchronous FSYN C time model. Given an arbitrarily distributed (yet connected) swarm of robots, the gathering problem on the grid is to locate all robots within a 2 × 2-sized area that is not known beforehand. Two robots are connected if they are vertical or horizontal neighbors on the grid. The locality constraint means that no global control, no compass, no global communication and only local vision is available; hence, a robot can only see its grid neighbors up to a constant L 1 -distance, which also limits its movements. A robot can move to one of its eight neighboring grid cells and if two or more robots move to the same location they are merged to be only one robot. The locality constraint is the significant challenging issue here, since robot movements must not harm the (only globally checkable) swarm connectivity. For solving the gathering problem, we provide a synchronous algorithm -executed by every robotwhich ensures that robots merge without breaking the swarm connectivity. In our model, robots can obtain a special state, which marks such a robot to be performing specific connectivity preserving movements in order to allow later merge operations of the swarm. Compared to the grid, for gathering in the Euclidean plane for the same robot and time model the best known upper bound is O(n 2 ) [DKL + 11].

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Solving the Robots Gathering Problem

Cited by 155 publications

References 14 publications

Efficient Algorithms for Detecting Regular Point Configurations

Efficient Algorithms for Detecting Regular Point Configurations

Connectivity preserving network transformers

Asymptotically Optimal Gathering on a Grid

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