Efficient Shape Formation by 3D Hybrid Programmable Matter: An Algorithm for Low Diameter Intermediate Structures
This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through pick-up, movement, and placement actions. The goal is to reconf...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
31.01.2024
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Subjects | |
Online Access | Get full text |
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Summary: | This paper considers the shape formation problem within the 3D hybrid model,
where a single agent with a strictly limited viewing range and the
computational capacity of a deterministic finite automaton manipulates passive
tiles through pick-up, movement, and placement actions. The goal is to
reconfigure a set of tiles into a specific shape termed an icicle. The icicle,
identified as a dense, hole-free structure, is strategically chosen to function
as an intermediate shape for more intricate shape formation tasks. It is
designed for easy exploration by a finite state agent, enabling the
identification of tiles that can be lifted without breaking connectivity.
Compared to the line shape, the icicle presents distinct advantages, including
a reduced diameter and the presence of multiple removable tiles. We propose an
algorithm that transforms an arbitrary initially connected tile structure into
an icicle in $\mathcal{O}(n^3)$ steps, matching the runtime of the line
formation algorithm from prior work. Our theoretical contribution is
accompanied by an extensive experimental analysis, indicating that our
algorithm decreases the diameter of tile structures on average. |
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DOI: | 10.48550/arxiv.2401.17734 |