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- W4287022963 abstract "We consider a discrete system of $n$ simple indistinguishable devices, called emph{agents}, forming a emph{connected} shape $S_I$ on a two-dimensional square grid. Agents are equipped with a linear-strength mechanism, called a emph{line move}, by which an agent can push a whole line of consecutive agents in one of the four directions in a single time-step. We study the problem of transforming an initial shape $S_I$ into a given target shape $S_F$ via a finite sequence of line moves in a distributed model, where each agent can observe the states of nearby agents in a Moore neighbourhood. Our main contribution is the first distributed connectivity-preserving transformation that exploits line moves within a total of $O(n log_2 n)$ moves, which is asymptotically equivalent to that of the best-known centralised transformations. The algorithm solves the emph{line formation problem} that allows agents to form a final straight line $S_L$, starting from any shape $ S_I $, whose emph{associated graph} contains a Hamiltonian path." @default.
- W4287022963 created "2022-07-25" @default.
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- W4287022963 date "2021-08-19" @default.
- W4287022963 modified "2023-09-28" @default.
- W4287022963 title "Distributed Transformations of Hamiltonian Shapes based on Line Moves" @default.
- W4287022963 doi "https://doi.org/10.48550/arxiv.2108.08953" @default.
- W4287022963 hasPublicationYear "2021" @default.
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