arXiv subjects

Joshua J. Daymude

Publications and source records attributed to Joshua J. Daymude.

26 records · Page 2Linked to original sources

arXiv2019

Simulation of Programmable Matter Systems Using Active Tile-Based Self-Assembly

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA) model was recently introduced as a platform to help study connections between various models of self-assembly. However, in this paper we present a result in which we use TA to simulate arbitrary systems within the amoebot model, a theoretical model of programmable matter in which the individual components are relatively simple state machines that are able to sense the states of their neighbors and to move via series of expansions and contractions. We show that for every amoebot system, there is a TA system capable of simulating the local information transmission built into amoebot particles, and that the TA "macrotiles" used to simulate its particles are capable of simulating movement (via attachment and detachment operations) while maintaining the necessary properties of amoebot particle systems. The TA systems are able to utilize only the local interactions of state changes and binding and unbinding along tile edges, but are able to fully simulate the dynamics of these programmable matter systems.

cs.ET↗

arXiv2019

A Local Stochastic Algorithm for Separation in Heterogeneous Self-Organizing Particle Systems

We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power. We consider heterogeneous particle systems of two different colors and prove that these systems can collectively separate into different color classes or integrate, indifferent to color. We accomplish both behaviors with the same fully distributed, local, stochastic algorithm. Achieving separation or integration depends only on a single global parameter determining whether particles prefer to be next to other particles of the same color or not; this parameter is meant to represent external, environmental influences on the particle system. The algorithm is a generalization of a previous distributed, stochastic algorithm for compression (PODC '16), which can be viewed as a special case of separation where all particles have the same color. It is significantly more challenging to prove that the desired behavior is achieved in the heterogeneous setting, however, even in the bichromatic case we focus on. This requires combining several new techniques, including the cluster expansion from statistical physics, a new variant of the bridging argument of Miracle, Pascoe and Randall (RANDOM '11), the high-temperature expansion of the Ising model, and careful probabilistic arguments.

cs.DC↗

arXiv2019

A Markov Chain Algorithm for Compression in Self-Organizing Particle Systems

In systems of programmable matter, we are given a collection of simple computation elements (or particles) with limited (constant-size) memory. We are interested in when they can self-organize to solve system-wide problems of movement, configuration and coordination. Here, we initiate a stochastic approach to developing robust distributed algorithms for programmable matter systems using Markov chains. We are able to leverage the wealth of prior work in Markov chains and related areas to design and rigorously analyze our distributed algorithms and show that they have several desirable properties. We study the compression problem, in which a particle system must gather as tightly together as possible, as in a sphere or its equivalent in the presence of some underlying geometry. More specifically, we seek fully distributed, local, and asynchronous algorithms that lead the system to converge to a configuration with small boundary. We present a Markov chain-based algorithm that solves the compression problem under the geometric amoebot model, for particle systems that begin in a connected configuration. The algorithm takes as input a bias parameter $λ$, where $λ> 1$ corresponds to particles favoring having more neighbors. We show that for all $λ> 2+\sqrt{2}$, there is a constant $α> 1$ such that eventually with all but exponentially small probability the particles are $α$-compressed, meaning the perimeter of the system configuration is at most $α\cdot p_{min}$, where $p_{min}$ is the minimum possible perimeter of the particle system. Surprisingly, the same algorithm can also be used for expansion when $0 < λ< 2.17$, and we prove similar results about expansion for values of $λ$ in this range. This is counterintuitive as it shows that particles preferring to be next to each other ($λ> 1$) is not sufficient to guarantee compression.

cs.DC↗

arXiv2018

A Stochastic Approach to Shortcut Bridging in Programmable Matter

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 a stochastic, distributed, local, asynchronous algorithm 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 trade-off using local interactions. 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 gives 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 also demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple extension of our previous stochastic algorithm for compression.

cs.DC↗

arXiv2017

Phototactic Supersmarticles

Smarticles, or smart active particles, are small robots equipped with only basic movement and sensing abilities that are incapable of rotating or displacing individually. We study the ensemble behavior of smarticles, i.e., the behavior a collective of these very simple computational elements can achieve, and how such behavior can be implemented using minimal programming. We show that an ensemble of smarticles constrained to remain close to one another (which we call a supersmarticle), achieves directed locomotion toward or away from a light source, a phenomenon known as phototaxing. We present experimental and theoretical models of phototactic supersmarticles that collectively move with a directed displacement in response to light. The motion of the supersmarticle is approximately Brownian, and is a result of chaotic interactions among smarticles. The system can be directed by introducing asymmetries among the individual smarticle's behavior, in our case by varying activity levels in response to light, resulting in supersmarticle biased motion.

cs.RO↗

arXiv2017

On the Runtime of Universal Coating for Programmable Matter

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.

cs.ET↗

arXiv2017

Improved Leader Election for Self-Organizing Programmable Matter

We consider programmable matter that consists of computationally limited devices (called particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention. We use the geometric amoebot model to describe such self-organizing particle systems, which defines how particles can actively move and communicate with one another. In this paper, we present an efficient local-control algorithm which solves the leader election problem in O(n) asynchronous rounds with high probability, where n is the number of particles in the system. Our algorithm relies only on local information --- particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system --- and requires only constant memory per particle.

cs.ET↗

arXiv2016

Leader Election and Shape Formation with Self-Organizing Programmable Matter

We consider programmable matter consisting of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way, and we investigate the feasibility of solving fundamental problems relevant for programmable matter. As a suitable model for such self-organizing particle systems, we will use a generalization of the geometric amoebot model first proposed in SPAA 2014. Based on the geometric model, we present efficient local-control algorithms for leader election and line formation requiring only particles with constant size memory, and we also discuss the limitations of solving these problems within the general amoebot model.

cs.ET↗