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We investigate the utility of employing multiple buffers in solving a classof rearrangement problems with pick-n-swap manipulation primitives. In thisproblem, objects stored randomly in a lattice are to be sorted using a robotarm with k>=1 swap spaces or buffers, capable of holding up to k objects on itsend-effector simultaneously. On the structural side, we show that the additionof each new buffer brings diminishing returns in saving the end-effector traveldistance while holding the total number of pick-n-swap operations at theminimum. This is due to an interesting recursive cycle structure in randomm-permutation, where the largest cycle covers over 60% of objects. On thealgorithmic side, we propose fast algorithms for 1D and 2D latticerearrangement problems that can effectively use multiple buffers to boostsolution optimality. Numerical experiments demonstrate the efficiency andscalability of our methods, as well as confirm the diminishing return structureas more buffers are employed.

On the Utility of Buffers in Pick-n-Swap Based Lattice Rearrangement