Distributed Transformations of Hamiltonian Shapes based on Line Moves
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We consider a discrete system of n simple indistinguishable devices, called agents, forming a connected shape S_I on a two-dimensional square grid. Agents are equipped with a linear-strength mechanism, called a 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 line formation problem that allows agents to form a final straight line S_L, starting from any shape S_I, whose associated graph contains a Hamiltonian path.
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