A divide-and-conquer algorithm decomposes atom reconfiguration into three 1D shuttling tasks, enabling O(sqrt N) total transportation cost and reliable solutions via the Gale-Ryser theorem for arbitrary geometries.
A theorem on flows in networks.Pacific Journal of Mathematics, 7(2):1073–1082, June 1957
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Square-root Time Atom Reconfiguration Plan for Lattice-shaped Mobile Tweezers
A divide-and-conquer algorithm decomposes atom reconfiguration into three 1D shuttling tasks, enabling O(sqrt N) total transportation cost and reliable solutions via the Gale-Ryser theorem for arbitrary geometries.