Computation Under Restricted Visibility

Bhagat, Subhash; Mukhopadhyaya, Krishnendu; Mukhopadhyaya, Srabani

doi:10.1007/978-3-030-11072-7_7

Cited by 8 publications

(7 citation statements)

References 28 publications

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“…In this article, we present an algorithm with runtime analysis to solve the gathering problem in the fully asynchronous model by assuming robots agree on one coordinate axis. Bhagat et al [21] studied the limited visibility model for robots and presented different geometric pattern formation problems under limited visibility.…”

Section: (Different and In Fact Smaller Than The Viewing Range Of One)mentioning

confidence: 99%

Time-Optimal Gathering under Limited Visibility with One-Axis Agreement

Poudel

Sharma

2021

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We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles following the well-celebrated classic oblivious robots model. We study the fundamental problem of gathering N autonomous robots on a plane, which requires all robots to meet at a single point (or to position within a small area) that is not known beforehand. We consider limited visibility under which robots are only able to see other robots up to a constant Euclidean distance and focus on the time complexity of gathering by robots under limited visibility. There exists an O(DG) time algorithm for this problem in the fully synchronous setting, assuming that the robots agree on one coordinate axis (say north), where DG is the diameter of the visibility graph of the initial configuration. In this article, we provide the first O(DE) time algorithm for this problem in the asynchronous setting under the same assumption of robots’ agreement with one coordinate axis, where DE is the Euclidean distance between farthest-pair of robots in the initial configuration. The runtime of our algorithm is a significant improvement since for any initial configuration of N≥1 robots, DE≤DG, and there exist initial configurations for which DG can be quadratic on DE, i.e., DG=Θ(DE2). Moreover, our algorithm is asymptotically time-optimal since the trivial time lower bound for this problem is Ω(DE).

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Section: (Different and In Fact Smaller Than The Viewing Range Of One)mentioning

confidence: 99%

Time-Optimal Gathering under Limited Visibility with One-Axis Agreement

Poudel

Sharma

2021

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“…Comparatively few investigations have focused on the limited visibility setting (see [4], for a recent survey). In this setting, it is typically assumed that the visibility graph associated with the initial robot configuration is connected.…”

Section: Related Workmentioning

confidence: 99%

Separating Bounded and Unbounded Asynchrony for Autonomous Robots

Kirkpatrick

Kostitsyna

Navarra

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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We consider distributed computations, by identical autonomous mobile entities, that solve the Point Convergence problem: given an arbitrary initial configuration of entities, disposed in the Euclidean plane, move in such a way that, for all ε > 0, a configuration is eventually reached and maintained in which the separation between all entities is at most ε. The problem has been previously studied in a variety of settings. Our study concerns the minimal assumptions under which entities, moving asynchronously with limited and unknown visibility range and subject to limited imprecision in measurements, can be guaranteed to converge in this way.We present an algorithm that solves Point Convergence, provided the degree of asynchrony is bounded by some arbitrarily large but fixed constant. This provides a strong positive answer to a decade old open question posed by Katreniak.We also prove that, in an otherwise comparable setting, Point Convergence is impossible with unbounded asynchrony. This serves to distinguish the power of bounded and unbounded asynchrony in the control of autonomous mobile entities, settling at the same time a long-standing question whether in the Euclidean plane synchronous entities are more powerful than asynchronous ones.

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“…Very few investigations have focused on the limited visibility setting, and among these none considers measurement errors (see [4], for a recent survey).…”

Section: Point Convergence Under Limited Visibilitymentioning

confidence: 99%

Separating Bounded and Unbounded Asynchrony for Autonomous Robots: Point Convergence with Limited Visibility

Kirkpatrick¹,

Kostitsyna²,

Navarra³

et al. 2021

Preprint

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Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is Point Convergence: given an arbitrary initial configuration of identical entities, disposed in the Euclidean plane, move in such a way that, for all ε > 0, a configuration in which the separation between all entities is at most ε is eventually reached and maintained.The problem has been previously studied in a variety of settings, including full visibility, exact measurements (like distances and angles), and synchronous activation of entities. Our study concerns the minimal assumptions under which entities, moving asynchronously with limited and unknown visibility range and subject to limited imprecision in measurements, can be guaranteed to converge in this way. We present an algorithm that solves Point Convergence, for entities in the plane, in such a setting, provided the degree of asynchrony is bounded: while any one entity is active, any other entity can be activated at most k times, for some arbitrarily large but fixed k. This provides a strong positive answer to a decade old open question posed by Katreniak.We also prove that in a comparable setting that permits unbounded asynchrony, Point Convergence in the plane is impossible, contingent on the natural assumption that algorithms maintain the (visible) connectivity among entities present in the initial configuration. This variant, that we call Cohesive Convergence, serves to distinguish the power of bounded and unbounded asynchrony in the control of autonomous mobile entities, settling at the same time a long-standing question whether in the Euclidean plane synchronously scheduled entities are more powerful than asynchronously scheduled entities.

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Computation Under Restricted Visibility

Cited by 8 publications

References 28 publications

Time-Optimal Gathering under Limited Visibility with One-Axis Agreement

Time-Optimal Gathering under Limited Visibility with One-Axis Agreement

Separating Bounded and Unbounded Asynchrony for Autonomous Robots

Separating Bounded and Unbounded Asynchrony for Autonomous Robots: Point Convergence with Limited Visibility

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