Leader election and local identifiers for three‐dimensional programmable matter

Gastineau, Nicolas; Mbarek, Nader; Togni, Olivier

doi:10.1002/cpe.6067

Cited by 8 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to election, they also assigned local identifiers to particles. (A subsequent paper by Gastineau et al [27] extended these results to a proposed three dimensional variant of the amoebot model and took ( ) time to elect a leader deterministically subject to constraints specific to their model.) The deterministic algorithm of Bazzi and Briones [3] also assumed common chirality.…”

Section: Related Workmentioning

confidence: 96%

“…During Algorithm DLE, all eligible points are at grid distance less than or equal to ( ) from (by definition of ( ) and Observation 5). Since particles occupy eligible points initially (by definition of 0 ) and only expand into eligible points (see lines [24][25][26][27][28][29], no particle occupies a point at grid distance > ( ) of when Algorithm DLE terminates.…”

Section: Reconnecting Leader Electionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Deterministic Leader Election for Programmable Matter

Dufoulon

Kutten

Moses

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

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.

show abstract

Section: Related Workmentioning

confidence: 96%

Section: Reconnecting Leader Electionmentioning

confidence: 99%

Efficient Deterministic Leader Election for Programmable Matter

Dufoulon

Kutten

Moses

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

show abstract

“…In addition to election, they also assigned local identifiers to particles. (A subsequent paper by Gastineau et al [28] extended these results to a proposed three dimensional variant of the amoebot model and took 𝑂 (𝑛) time to elect a leader deterministically subject to constraints specific to their model.) The deterministic 1 There are some partial exceptions.…”

Section: Related Workmentioning

confidence: 96%

Efficient Deterministic Leader Election for Programmable Matter

Dufoulon¹,

Kutten²,

Moses³

2021

Preprint

View full text Add to dashboard Cite

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 𝑛, where 𝑛 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?"

show abstract

“…A different approach to the coating problem is considered in the field of swarm robotics, where the objective is a non-uniform spatial distribution of robots around objects that are too heavy to be lifted alone [24]. The problem of leader election by generic agents in the FCC lattice is considered in [12]; the authors provide an algorithm that requires only constant memory space but is restricted to specific initial shapes.…”

Section: Related Workmentioning

confidence: 99%

Universal Coating in the 3D Hybrid Model

Kostitsyna¹,

Liedtke²,

Scheideler³

2023

Preprint

View full text Add to dashboard Cite

Motivated by the prospect of nano-robots that assist human physiological functions at the nanoscale, we investigate the coating problem in the three-dimensional model for hybrid programmable matter. In this model, a single agent with strictly limited viewing range and the computational capability of a deterministic finite automaton can act on passive tiles by picking up a tile, moving, and placing it at some spot. The goal of the coating problem is to fill each node of some surface graph of size n with a tile. We first solve the problem on a restricted class of graphs with a single tile type, and then use constantly many tile types to encode this graph in certain surface graphs capturing the surface of 3D objects. Our algorithm requires O(n 2 ) steps, which is worst-case optimal compared to an agent with global knowledge and no memory restrictions.

show abstract

Leader election and local identifiers for three‐dimensional programmable matter

Cited by 8 publications

References 18 publications

Efficient Deterministic Leader Election for Programmable Matter

Efficient Deterministic Leader Election for Programmable Matter

Efficient Deterministic Leader Election for Programmable Matter

Universal Coating in the 3D Hybrid Model

Contact Info

Product

Resources

About