Improved Leader Election for Self-organizing Programmable Matter

Daymude, Joshua J.; Gmyr, Robert; Richa, Andréa W.; Scheideler, Christian; Strothmann, Thim

doi:10.1007/978-3-319-72751-6_10

“…As our main contribution in this paper, we investigate the runtime of our algorithm and prove that our algorithm terminates within a linear number of rounds with high probability. This result relies, in part, on an update to the leader election protocol used in [3] which is fully defined and analyzed in [20]. We also present a matching linear lower bound for any local-control coating algorithm (i.e., one which uses only local information in its execution) that holds with high probability.…”

Section: Our Contributionsmentioning

confidence: 99%

On the runtime of universal coating for programmable matter

Daymude

¹

,

Derakhshandeh

²

,

Gmyr

³

et al. 2017

Self Cite

View full text Add to dashboard Cite

Abstract. Imagine coating buildings and bridges with smart particles (also coined smart paint) that monitor structural integrity and sense and report on traffic and wind loads, leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time. In this paper, we study the problem of uniformly coating objects of arbitrary shape in the context of self-organizing programmable matter, i.e., programmable matter which consists of simple computational elements called particles that can establish and release bonds and can actively move in a self-organized way. Particles are anonymous, have constant-size memory, and utilize only local interactions in order to coat an object. We continue the study of our Universal Coating algorithm by focusing on its runtime analysis, showing that our algorithm terminates within a linear number of rounds with high probability. We also present a matching linear lower bound that holds with high probability. We use this lower bound to show a linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information, which implies that our algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of our algorithm may be better than linear in practice.

show abstract

“…In order to formally prove with high probability results on the runtime of the universal coating algorithm, we introduced a variant of our leader election protocol under the amoebot model which provably elects a leader in O(n) asynchronous rounds, w.h.p. 7 [20]. This gives the following runtime bound.…”

Section: First Layer: Complaint-based Coating and Leader Electionmentioning

confidence: 96%

On the Runtime of Universal Coating for Programmable Matter

Derakhshandeh

¹

,

Gmyr

²

,

Porter

³

et al. 2016

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. Imagine coating buildings and bridges with smart particles (also coined smart paint) that monitor structural integrity and sense and report on traffic and wind loads, leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time. In this paper, we study the problem of uniformly coating objects of arbitrary shape in the context of self-organizing programmable matter, i.e., programmable matter which consists of simple computational elements called particles that can establish and release bonds and can actively move in a self-organized way. Particles are anonymous, have constant-size memory, and utilize only local interactions in order to coat an object. We continue the study of our Universal Coating algorithm by focusing on its runtime analysis, showing that our algorithm terminates within a linear number of rounds with high probability. We also present a matching linear lower bound that holds with high probability. We use this lower bound to show a linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information, which implies that our algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of our algorithm may be better than linear in practice.

show abstract

“…In this appendix we present a way to reduce the required number of rounds in order that this algorithm finishes its execution (by using the S-contraction algorithm). In the remaining part of this appendix, the leader election algorithm from [5] will be called the general leader election Algorithm 4 A spanning-tree algorithm for a particle p.…”

Section: H Combining the S-contraction Algorithm With A General Leadementioning

confidence: 99%

“…The way how the messages are re-transmitted in the algorithm of Daymude et al[5] (square: articulation; dashed arrow: message transmitted along the border; simple arrow: message transmitted along the hole).…”

mentioning

confidence: 99%

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

Gastineau

¹

,

Mbarek

²

,

Togni

³

2019

Algorithms for Sensor Systems

View full text Add to dashboard Cite

The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local positions of neighborhood particles. Under these assumptions, we describe a new leader election algorithm affecting a variable to the particles, called the k-local identifier, in such a way that particles at close distance have each a different k-local identifier. For all the presented algorithms, the particles only need a O(1)-memory space.there exists a probabilistic algorithm that determine a leader (and in particular for a ring) with probability 1 [5].Several projects aim to build programmable matter prototypes. One of such projects [20,23], financed by the french National Agency for Research, aims to build cuboctahedral particles able to deform them-selves in order to move. This project can be split in two phases, one consists in manufacturing the hardware of prototype matters, the second consists in proposing algorithms for programmable matter. The final goal of this project is to sculpt a shape-memory polymer sheet with programmable matter. In the continuity of the algorithm phase of this project [20], we propose algorithms for the self-configuration, i.e., in order to create identifiers and spanning trees.In the context of programmable matter [3,4,14,18,23,24], it is supposed that a network can contain several millions of modules and that each module has possibly a nano-centimeter size. These two facts lead us to believe that even a O(log(n))-space memory for each module, n being the number of modules, is not technically possible. Also, because of the large number of modules, it can be very challenging and time consuming to implement a unique identity to the modules when they are created. In this context, we suppose that the modules can not store a unique identity, i.e., that the network is anonymous. In this paper we propose deterministic O(1)-space memory algorithms to determine a leader in the network and to create k-local identifiers of the particles. A k-local identifier is a variable affected to each module of the network which is different for every two modules at distance at most k. Note that leader election [5, 13] plays a significant role in numerous problems of programmable matter.Our contribution is the following: we introduce a leader election algorithm based on local computations and simple to implement. This algorithm works when the structure the particles form has no hole (see Section 3). Also, since the algorithm can be described as a sequence of local computations, its limits (message complexity, required memory-space, etc) are easy to analyze. We present a distributed algorithm to construct a spanning tree in the context of programmable matter and, also, a distributed algorithm to re-organize the port numbers of the particles. Finally, we presen...

show abstract

Improved Leader Election for Self-organizing Programmable Matter

Cited by 47 publications

References 37 publications

On the runtime of universal coating for programmable matter

On the runtime of universal coating for programmable matter

On the Runtime of Universal Coating for Programmable Matter

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

Contact Info

Product

Resources

About