Thim Strothmann

Brief announcement: amoebot -- a new model for programmable matter

The term programmable matter refers to matter which has the ability to change its physical properties (shape, density, moduli, conductivity, optical properties, etc.) in a programmable fashion, based upon user input or autonomous sensing. This has many applications like smart materials, autonomous monitoring and repair, and minimal invasive surgery, so there is a high relevance of this topic to industry and society in general. While programmable matter has just been science fiction more than two decades ago, a large amount of research activities can now be seen in this field in the recent years. Often programmable matter is envisioned, as a very large number of small locally interacting computational \emph{particles}. We propose the Amoebot model, a new model which builds upon this vision of programmable matter. Inspired by the behavior of amoeba, the Amoebot model offers a versatile framework to model self-organizing particles and facilitates rigorous algorithmic research in the area of programmable matter.

Leader Election and Shape Formation with Self-organizing Programmable Matter

In this paper 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 model for such self-organizing particle systems, we will use a generalization of the geometric amoebot model first proposed ini¾?[21]. 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.

An Algorithmic Framework for Shape Formation Problems in Self-Organizing Particle Systems

This material is based on work in progress. Imagine that we had a piece of matter that can change its physical properties like shape, density, conductivity, or color in a programmable fashion based on either user input or autonomous sensing. This is the vision behind what is commonly known as programmable matter. Programmable matter is the subject of many recent novel distributed computing proposals --- ranging from DNA tiles, shape-changing molecules, and synthetic cells, to reconfigurable modular robotics --- each pursuing solutions for specific application scenarios with their own, special capabilities and constraints.

Universal Shape Formation for Programmable Matter

We envision programmable matter consisting of systems of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention. Central problems for these particle systems are shape formation and coating problems. In this paper, we present a universal shape formation algorithm which takes an arbitrary shape composed of a constant number of equilateral triangles of unit size and lets the particles build that shape at a scale depending on the number of particles in the system. Our algorithm runs in O(√n) asynchronous execution rounds, where

Universal coating for programmable matter

n

On Stabilizing Departures in Overlay Networks

is the number of particles in the system, provided we start from a well-initialized configuration of the particles. This is optimal in a sense that for any shape deviating from the initial configuration, any movement strategy would require Ω(√n) rounds in the worst case (over all asynchronous activations of the particles). Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.

On the runtime of universal coating for programmable matter

The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without requiring direct access to that spot. We study the universal coating problem in the context of self-organizing programmable matter consisting of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way. Based on that matter, we present a worst-case work-optimal universal coating algorithm that uniformly coats any object of arbitrary shape and size that allows a uniform coating. Our particles are anonymous, do not have any global information, have constant-size memory, and utilize only local interactions.

Improved Leader Election for Self-organizing Programmable Matter

A fundamental problem for peer-to-peer systems is to maintain connectivity while nodes are leaving, i.e., the nodes requesting to leave the peer-to-peer system are excluded from the overlay network without affecting its connectivity. There are a number of studies for safe node exclusion if the overlay is in a well-defined state initially. Surprisingly, the problem is not formally studied yet for the case in which the overlay network is in an arbitrary initial state, i.e., when looking for a self-stabilizing solution for excluding leaving nodes. We study this problem in two variants: the Finite Departure Problem ( \(\mathcal{FDP}\) ) and the Finite Sleep Problem ( \(\mathcal{FSP}\) ). In the \(\mathcal{FDP}\) the leaving nodes have to irrevocably decide when it is safe to leave the network, whereas in the \(\mathcal{FSP}\), this leaving decision does not have to be final: the nodes may resume computation if necessary. We show that there is no self-stabilizing distributed algorithm for the \(\mathcal{FDP}\), even in a synchronous message passing model. To allow a solution, we introduce an oracle called \(\mathcal{NIDEC}\) and show that it is sufficient even for the asynchronous message passing model by proposing an algorithm that can solve the \(\mathcal{FDP}\) using \(\mathcal{NIDEC}\). We also show that a solution to the \(\mathcal{FSP}\) does not require an oracle.

Towards a Universal Approach for the Finite Departure Problem in Overlay Networks

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.

On the Runtime of Universal Coating for 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 \(\mathcal {O}(n)\) 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.