Convex Hull Formation for Programmable Matter

Daymude, Joshua J.; Gmyr, Robert; Hinnenthal, Kristian; Kostitsyna, Irina; Scheideler, Christian; Richa, Andréa W.

doi:10.1145/3369740.3372916

Cited by 21 publications

(21 citation statements)

References 28 publications

(40 reference statements)

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“…In order to provide a concrete motivation why our proposed extension of the amoebot model via reconfigurable circuits has some benefits over the standard model, we first present a fast algorithm for the leader election problem (which is an extensively researched problem within the geometric amoebot model [2,8,12,18,20,30]) and then describe how using circuits can be helpful in shape transformation, which may potentially lead to faster algorithms for the (extensively researched) shape formation problem [7,10,14,12,30].…”

Section: Why Care About Circuits?mentioning

confidence: 99%

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Accelerating Amoebots via Reconfigurable Circuits

Feldmann,

Padalkin,

Scheideler

et al. 2021

Preprint

Self Cite

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We consider an extension to the geometric amoebot model that allows amoebots to form so-called circuits. Given a connected amoebot structure, a circuit is a subgraph formed by the amoebots that permits the instant transmission of signals. We show that such an extension allows for significantly faster solutions to a variety of problems related to programmable matter. More specifically, we provide algorithms for leader election, consensus, compass alignment, chirality agreement and shape recognition. Leader election can be solved in Θ(log n) rounds, w.h.p., consensus in O(1) rounds and both, compass alignment and chirality agreement, can be solved in O(log n) rounds, w.h.p. For shape recognition, the amoebots have to decide whether the amoebot structure forms a particular shape. We show how the amoebots can detect a parallelogram with linear and polynomial side ratio within Θ(log n) rounds, w.h.p. Finally, we show that the amoebots can detect a shape composed of triangles within O(1) rounds, w.h.p.

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Section: Why Care About Circuits?mentioning

confidence: 99%

“…Their algorithm requires O(n) rounds. Further publications include shape formation [12,10,14,30,7], gathering [4], and object coating [13,9].…”

Section: Related Workmentioning

confidence: 99%

Accelerating Amoebots via Reconfigurable Circuits

Feldmann,

Padalkin,

Scheideler

et al. 2021

Preprint

Self Cite

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“…In this context, it is important to find a good balance between the preservation of the information and the legibility of the visualization [12]. Considering a polygon as input geometry, a basic technique for simplification and schematization is the convex hull [6,18,26,45]. An approach for rectilinear input polygons are tight rectilinear hulls [9].…”

Section: Related Workmentioning

confidence: 99%

Shortcut Hulls: Vertex-restricted Outer Simplifications of Polygons

Bonerath¹,

Haunert²,

Mitchell³

et al. 2021

Preprint

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Let P be a crossing-free polygon and C a set of shortcuts, where each shortcut is a directed straight-line segment connecting two vertices of P . A shortcut hull of P is another crossing-free polygon that encloses P and whose oriented boundary is composed of elements from C. Shortcut hulls find their application in geo-related problems such as the simplification of contour lines. We aim at a shortcut hull that linearly balances the enclosed area and perimeter. If no holes in the shortcut hull are allowed, the problem admits a straight-forward solution via shortest paths. For the more challenging case that the shortcut hull may contain holes, we present a polynomial-time algorithm that is based on computing a constrained, weighted triangulation of the input polygon's exterior. We use this problem as a starting point for investigating further variants, e.g., restricting the number of edges or bends. We demonstrate that shortcut hulls can be used for drawing the rough extent of point sets as well as for the schematization of polygons.

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“…In this model, each particle can move from one grid point of a triangular grid to a neighboring grid point in a way that resembles an amoeba. Many problems of interest were addressed, including coating of materials [7,16,17], bridge building [1], energy distribution [12], shape formation [5,8,14,15,20,21], and shape recovery [19]. Towards solving these problems, a dominant strategy has been to elect a unique leader among the particles, which then coordinates all the movements.…”

Section: Introductionmentioning

confidence: 99%

Efficient Deterministic Leader Election for Programmable Matter

Dufoulon

Kutten

Moses

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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It was suggested that a programmable matter system (composed of multiple computationally weak mobile particles) should remain connected at all times since otherwise, reconnection is difficult and may be impossible. At the same time, it was not clear that allowing the system to disconnect carried a significant advantage in terms of time complexity. We demonstrate for a fundamental task, that of leader election, an algorithm where the system disconnects and then reconnects automatically in a non-trivial way (particles can move far away from their former neighbors and later reconnect to others). Moreover, the runtime of the temporarily disconnecting deterministic leader election algorithm is linear in the diameter. Hence, the disconnecting -reconnecting algorithm is as fast as previous randomized algorithms. When comparing to previous deterministic algorithms, we note that some of the previous work assumed weaker schedulers. Still, the runtime of all the previous deterministic algorithms that did not assume special shapes of the particle system (shapes with no holes) was at least quadratic in , where is the number of particles in the system. (Moreover, the new algorithm is even faster in some parameters than the deterministic algorithms that did assume special initial shapes.)Since leader election is an important module in algorithms for various other tasks, the presented algorithm can be useful for speeding up other algorithms under the assumption of a strong scheduler. This leaves open the question: "can a deterministic algorithm be as fast as the randomized ones also under weaker schedulers?" CCS CONCEPTS• Theory of computation → Self-organization; Distributed algorithms; • Computing methodologies → Mobile agents.

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Convex Hull Formation for Programmable Matter

Cited by 21 publications

References 28 publications

Accelerating Amoebots via Reconfigurable Circuits

Accelerating Amoebots via Reconfigurable Circuits

Shortcut Hulls: Vertex-restricted Outer Simplifications of Polygons

Efficient Deterministic Leader Election for Programmable Matter

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