@inproceedings{54807,
  abstract     = {{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 𝒪(n³) 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.}},
  author       = {{Hinnenthal, Kristian and Liedtke, David Jan and Scheideler, Christian}},
  booktitle    = {{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)}},
  editor       = {{Casteigts, Arnaud and Kuhn, Fabian}},
  isbn         = {{978-3-95977-315-7}},
  issn         = {{1868-8969}},
  keywords     = {{Programmable Matter, Shape Formation, 3D Model, Finite Automaton}},
  pages        = {{15:1–15:20}},
  publisher    = {{Schloss Dagstuhl – Leibniz-Zentrum für Informatik}},
  title        = {{{Efficient Shape Formation by 3D Hybrid Programmable Matter: An Algorithm for Low Diameter Intermediate Structures}}},
  doi          = {{10.4230/LIPIcs.SAND.2024.15}},
  volume       = {{292}},
  year         = {{2024}},
}

@inbook{54802,
  abstract     = {{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 O(n^2) steps, which is worst-case optimal compared to an agent with global knowledge and no memory restrictions.}},
  author       = {{Kostitsyna, Irina and Liedtke, David Jan and Scheideler, Christian}},
  booktitle    = {{Structural Information and Communication Complexity}},
  editor       = {{Emek, Yuval}},
  isbn         = {{9783031606021}},
  issn         = {{0302-9743}},
  keywords     = {{Programmable Matter, Coating, Finite Automaton, 3D}},
  publisher    = {{Springer Nature Switzerland}},
  title        = {{{Universal Coating by 3D Hybrid Programmable Matter}}},
  doi          = {{10.1007/978-3-031-60603-8_21}},
  year         = {{2024}},
}

@article{1813,
  author       = {{P. Fekete, Sandor and W. Richa, Andrea and Römer, Kay and Scheideler, Christian}},
  journal      = {{SIGACT News}},
  number       = {{2}},
  pages        = {{87----94}},
  title        = {{{Algorithmic Foundations of Programmable Matter Dagstuhl Seminar 16271}}},
  doi          = {{10.1145/3106700.3106713}},
  year         = {{2017}},
}