Connor, Matthew, Michail, Othon 
ORCID: 0000-0002-6234-3960 and Potapov, Igor
(2021)
Centralised Connectivity-Preserving Transformations for Programmable
Matter: A Minimal Seed Approach.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12961 .
pp. 45-60.
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2108.09250v1.pdf - Submitted version Download (1MB) | Preview |
Abstract
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.
| Item Type: | Article |
|---|---|
| Additional Information: | 22 pages, 10 figures |
| Uncontrolled Keywords: | cs.DC, cs.DC |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 02 Sep 2021 08:15 |
| Last Modified: | 18 Jan 2023 21:30 |
| DOI: | 10.1007/978-3-030-89240-1_4 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3135611 |
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