Efficient Algorithms for Detecting Regular Point Configurations

Anderegg, Luzi; Cieliebak, Mark; Prencipe, Giuseppe

doi:10.1007/11560586_4

Cited by 5 publications

(13 citation statements)

References 5 publications

(5 reference statements)

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“…If the points in P are not on a line, then the Weber point always exists, and it is unique [53]. Moreover, it is easy to verify (see also [2]) that the following holds.…”

Section: Basic Notationmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Computing by Mobile Robots: Gathering

Cieliebak¹,

Flocchini²,

Prencipe³

et al. 2012

SIAM J. Comput.

Self Cite

204

147

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Abstract. Consider a set of n > 2 identical mobile computational entities in the plane, called robots, operating in Look-Compute-Move cycles, without any means of direct communication. The Gathering Problem is the primitive task of all entities gathering in finite time at a point not fixed in advance, without any external control. The problem has been extensively studied in the literature under a variety of strong assumptions (e.g., synchronicity of the cycles, instantaneous movements, complete memory of the past, common coordinate system, etc.). In this paper we consider the setting without those assumptions, that is, when the entities are oblivious (i.e., they do not remember results and observations from previous cycles), disoriented (i.e., have no common coordinate system), and fully asynchronous (i.e., no assumptions exist on timing of cycles and activities within a cycle). The existing algorithmic contributions for such robots are limited to solutions for n ≤ 4 or for restricted sets of initial configurations of the robots; the question of whether such weak robots could deterministically gather has remained open. In this paper, we prove that indeed the Gathering Problem is solvable, for any n > 2 and any initial configuration, even under such restrictive conditions.

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“…If the points in P are not on a line, then the Weber point always exists, and it is unique [53]. Moreover, it is easy to verify (see also [2]) that the following holds.…”

Section: Basic Notationmentioning

confidence: 99%

“…. , α n−1 , using the algorithm described in [2], it is possible to efficiently determine whether there exists a point c such that σ ∈ SA(P, c). In other words, there exists an efficient way to determine whether P is biangular if the two angles α and β are given.…”

Section: There Exists a Set S ⊂ P Of Points |S|mentioning

confidence: 99%

Distributed Computing by Mobile Robots: Gathering

Cieliebak¹,

Flocchini²,

Prencipe³

et al. 2012

SIAM J. Comput.

Self Cite

204

147

View full text Add to dashboard Cite

show abstract

“…If the Weber point can be computed, it is simple to devise a robot protocol that solves gathering: all robots simply move toward the Weber point. Unfortunately, computing the Weber point is known to be difficult and was solved in special cases such as regular polygons [3], line [8], and a number of symmetric and regular configurations [6]. A key result of this paper is a technique to compute the Weber point of a newly defined class of configurations, referred in the sequel as quasi-regular configurations, which are less symmetric than both symmetric and regular configurations.…”

Section: Reference Model Chirality Multiplicitymentioning

confidence: 99%

Brief Announcement: Wait-Free Gathering of Mobile Robots

Bouzid

Das

Tixeuil

2012

Lecture Notes in Computer Science

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“…Our result may be interesting in its own right, since the problem of finding Weber points has been solved up to now for only few other patterns (e.g. regular polygon [2], a line [3]).…”

Section: Introductionmentioning

confidence: 97%

Robot Networks with Homonyms: The Case of Patterns Formation

Bouzid

Lamani

2011

Lecture Notes in Computer Science

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Abstract. In this paper, we consider the problem of formation of a series of geometric patterns [4] by a network of oblivious mobile robots that communicate only through vision. So far, the problem has been studied in models where robots are either assumed to have distinct identifiers or to be completely anonymous. To generalize these results and to better understand how anonymity affects the computational power of robots, we study the problem in a new model, introduced recently in [5], in which n robots may share up to 1 ≤ h ≤ n different identifiers. We present necessary and sufficient conditions, relating symmetricity and homonymy, that makes the problem solvable. We also show that in the case where h = n, making the identifiers of robots invisible does not limit their computational power. This contradicts a result of [4]. To present our algorithms, we use a function that computes the Weber point for many regular and symmetric configurations. This function is interesting in its own right, since the problem of finding Weber points has been solved up to now for only few other patterns.

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Efficient Algorithms for Detecting Regular Point Configurations

Cited by 5 publications

References 5 publications

Distributed Computing by Mobile Robots: Gathering

Distributed Computing by Mobile Robots: Gathering

Brief Announcement: Wait-Free Gathering of Mobile Robots

Robot Networks with Homonyms: The Case of Patterns Formation

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