TY - GEN
T1 - Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid
AU - Yamada, Ryonosuke
AU - Yamauchi, Yukiko
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP18H03202 and JST SICORP Grant Number JPMJSC1806, Japan.
Funding Information:
Funding This work was supported by JSPS KAKENHI Grant SICORP Grant Number JPMJSC1806, Japan.
Publisher Copyright:
© Ryonosuke Yamada and Yukiko Yamauchi; licensed under Creative Commons License CC-BY 4.0
PY - 2022/4/1
Y1 - 2022/4/1
N2 - We consider search in a finite 3D cubic grid by a metamorphic robotic system (MRS), that consists of anonymous modules. A module can perform a sliding and rotation while the whole modules keep connectivity. As the number of modules increases, the variety of actions that the MRS can perform increases. The search problem requires the MRS to find a target in a given finite field. Doi et al. (SSS 2018) demonstrate a necessary and sufficient number of modules for search in a finite 2D square grid. We consider search in a finite 3D cubic grid and investigate the effect of common knowledge. We consider three different settings. First, we show that three modules are necessary and sufficient when all modules are equipped with a common compass, i.e., they agree on the direction and orientation of the x, y, and z axes. Second, we show that four modules are necessary and sufficient when all modules agree on the direction and orientation of the vertical axis. Finally, we show that five modules are necessary and sufficient when all modules are not equipped with a common compass. Our results show that the shapes of the MRS in the 3D cubic grid have richer structure than those in the 2D square grid.
AB - We consider search in a finite 3D cubic grid by a metamorphic robotic system (MRS), that consists of anonymous modules. A module can perform a sliding and rotation while the whole modules keep connectivity. As the number of modules increases, the variety of actions that the MRS can perform increases. The search problem requires the MRS to find a target in a given finite field. Doi et al. (SSS 2018) demonstrate a necessary and sufficient number of modules for search in a finite 2D square grid. We consider search in a finite 3D cubic grid and investigate the effect of common knowledge. We consider three different settings. First, we show that three modules are necessary and sufficient when all modules are equipped with a common compass, i.e., they agree on the direction and orientation of the x, y, and z axes. Second, we show that four modules are necessary and sufficient when all modules agree on the direction and orientation of the vertical axis. Finally, we show that five modules are necessary and sufficient when all modules are not equipped with a common compass. Our results show that the shapes of the MRS in the 3D cubic grid have richer structure than those in the 2D square grid.
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U2 - 10.4230/LIPIcs.SAND.2022.20
DO - 10.4230/LIPIcs.SAND.2022.20
M3 - Conference contribution
AN - SCOPUS:85130775621
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022
A2 - Aspnes, James
A2 - Michail, Othon
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022
Y2 - 28 March 2022 through 30 March 2022
ER -