Leader Election and Shape Formation with Self-organizing Programmable Matter

Derakhshandeh, Zahra; Gmyr, Robert; Strothmann, Thim; Bazzi, Rida A.; Richa, Andréa W.; Scheideler, Christian

doi:10.1007/978-3-319-21999-8_8

Cited by 52 publications

(120 citation statements)

References 44 publications

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“…Our proposed leader election algorithm (Algorithm 1) works even if V (P ) contains a particle p which is an articulation. However, in contrast with the leader election algorithm from Derakhshandeh et al [8], Algorithm 1 does not work if P has holes. In the remaining part of this paper, Algorithm 1 is called the S-contraction algorithm.…”

Section: Leader Electionmentioning

confidence: 99%

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

Gastineau

Mbarek

Togni

2019

Algorithms for Sensor Systems

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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...

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Section: Leader Electionmentioning

confidence: 99%

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

Gastineau

Mbarek

Togni

2019

Algorithms for Sensor Systems

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“…when S.canSendT oken() returns true. 1 If a line of particles is not readily available, one can easily build one following the algorithm presented in [4] concurrently with the binary counting procedure -i.e., there is no need for synchronization of the phases, as it happens in the matrix-vector multiplication algorithm presented below. S.sendT oken()…”

Section: Algorithm 1 Binary Counter Particlementioning

confidence: 99%

“…However, they also require computations resembling those done by traditional computers to process information and make decisions. Work so far using the geometric amoebot model for self-organizing particle systems has focused on spatial configuration, including demonstrating efficient programmable matter algorithms for * This work was supported in part by NSF under Awards CCF-1353089 and CCF-1422603, and matching NSF REU awards; this work was conducted while the first author was an undergraduate student at ASU shape formation, coating, and compression (e.g., [2], [3], [4], [5]).…”

Section: Introductionmentioning

confidence: 99%

Collaborative Computation in Self-organizing Particle Systems

Porter

Richa

2018

Unconventional Computation and Natural Computation

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Many forms of programmable matter have been proposed for various tasks. We use an abstract model of selforganizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials for engineering or programmable cells for medical uses. Previous research using this model has focused on shape formation and other spatial configuration problems (e.g., coating and compression). In this work we study foundational computational tasks that exceed the capabilities of the individual constant size memory of a particle, such as implementing a counter and matrix-vector multiplication. These tasks represent new ways to use these self-organizing systems, which, in conjunction with previous shape and configuration work, make the systems useful for a wider variety of tasks. They can also leverage the distributed and dynamic nature of the self-organizing system to be more efficient and adaptable than on traditional linear computing hardware. Finally, we demonstrate applications of similar types of computations with selforganizing systems to image processing, with implementations of image color transformation and edge detection algorithms.

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“…We recall the main properties of the amoebot model [5,12], an abstract model for programmable matter that provides a framework for rigorous algorithmic research on nano-scale systems. We represent programmable matter as a collection of individual computational units known as particles.…”

Section: The Amoebot Modelmentioning

confidence: 99%

“…Any Markov chain for particle systems that inherently relies on non-local moves of particles or has transition probabilities relying on non-local information cannot be executed by a local, distributed algorithm. Moreover, most distributed algorithms for amoebot systems are not stochastic and thus cannot be described as Markov chains; see, e.g., the mostly deterministic algorithms in [12,11].…”

Section: From M To a Distributed Local Algorithmmentioning

confidence: 99%

A Stochastic Approach to Shortcut Bridging in Programmable Matter

Arroyo

Cannon

Daymude

et al. 2017

Lecture Notes in Computer Science

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In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and configuration. In this paper, we consider stochastic, distributed, local, asynchronous algorithms for "shortcut bridging", in which particles self-assemble bridges over gaps that simultaneously balance minimizing the length and cost of the bridge. Army ants of the genus Eciton have been observed exhibiting a similar behavior in their foraging trails, dynamically adjusting their bridges to satisfy an efficiency tradeoff using local interactions [22]. Using techniques from Markov chain analysis, we rigorously analyze our algorithm, show it achieves a near-optimal balance between the competing factors of path length and bridge cost, and prove that it exhibits a dependence on the angle of the gap being "shortcut" similar to that of the ant bridges. We also present simulation results that qualitatively compare our algorithm with the army ant bridging behavior. Our work presents a plausible explanation of how convergence to globally optimal configurations can be achieved via local interactions by simple organisms (e.g., ants) with some limited computational power and access to random bits. The proposed algorithm demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple extension of a stochastic algorithm for compression [5].

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Leader Election and Shape Formation with Self-organizing Programmable Matter

Cited by 52 publications

References 44 publications

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

Collaborative Computation in Self-organizing Particle Systems

A Stochastic Approach to Shortcut Bridging in Programmable Matter

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