Centralised Connectivity-Preserving Transformations for Programmable Matter: A Minimal Seed Approach
| Autor: | Othon Michail, Igor Potapov, Matthew Connor |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Square tiling General Computer Science Open problem Orbital node Topology Theoretical Computer Science Programmable matter Transformation (function) Computer Science - Distributed Parallel and Cluster Computing Line (geometry) Perpendicular Distributed Parallel and Cluster Computing (cs.DC) Focus (optics) ComputingMethodologies_COMPUTERGRAPHICS Mathematics |
| Zdroj: | Algorithms for Sensor Systems ISBN: 9783030892395 ALGOSENSORS Theoretical Computer Science Algorithms for Sensor Systems |
| DOI: | 10.1007/978-3-030-89240-1_4 |
| Popis: | We study a model of programmable matter systems consisting of $n$ devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial shape A into a target shape B. We investigate the class of shapes which can be constructed in such a scenario under the additional constraint of maintaining global connectivity at all times. We focus on the scenario of transforming nice shapes, a class of shapes consisting of a central line $L$ where for all nodes $u$ in $S$ either $u \in L$ or $u$ is connected to $L$ by a line of nodes perpendicular to $L$. We prove that by introducing a minimal 3-node seed it is possible for the canonical shape of a line of $n$ nodes to be transformed into a nice shape of $n-1$ nodes. We use this to show that a 4-node seed enables the transformation of nice shapes of size $n$ into any other nice shape of size $n$ in $O(n^2)$ time. We leave as an open problem the expansion of the class of shapes which can be constructed using such a seed to include those derived from nice shapes. Comment: 22 pages, 10 figures |
| Databáze: | OpenAIRE |
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