Universal Coating by 3D Hybrid Programmable Matter

Motivated by the prospect of nano-robots that assist human physiological functions at the nanoscale, we investigate the coating problem in the three-dimensional model for hybrid programmable matter. In this model, a single agent with strictly limited viewing range and the computational capability of...

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Bibliographic Details
Published inarXiv.org
Main Authors Kostitsyna, Irina, Liedtke, David, Scheideler, Christian
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.02.2024
Subjects
Algorithms
Coating
Graphs
Three dimensional models
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Summary:Motivated by the prospect of nano-robots that assist human physiological functions at the nanoscale, we investigate the coating problem in the three-dimensional model for hybrid programmable matter. In this model, a single agent with strictly limited viewing range and the computational capability of a deterministic finite automaton can act on passive tiles by picking up a tile, moving, and placing it at some spot. The goal of the coating problem is to fill each node of some surface graph of size \(n\) with a tile. We first solve the problem on a restricted class of graphs with a single tile type, and then use constantly many tile types to encode this graph in certain surface graphs capturing the surface of 3D objects. Our algorithm requires \(\mathcal{O}(n^2)\) steps, which is worst-case optimal compared to an agent with global knowledge and no memory restrictions.
ISSN:2331-8422