Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rearrangement on Lattices with Pick-n-Swaps: Optimality Structures and
  Efficient Algorithms   We propose and study a class of rearrangement problems under a novel
pick-n-swap prehensile manipulation model, in which a robotic manipulator,
capable of carrying an item and making item swaps, is tasked to sort items
stored in lattices of variable dimensions in a time-optimal manner. We
systematically analyze the intrinsic optimality structure, which is fairly rich
and intriguing, under different levels of item distinguishability (fully
labeled, where each item has a unique label, or partially labeled, where
multiple items may be of the same type) and different lattice dimensions.
Focusing on the most practical setting of one and two dimensions, we develop
low polynomial time cycle-following based algorithms that optimally perform
rearrangements on 1D lattices under both fully- and partially-labeled settings.
On the other hand, we show that rearrangement on 2D and higher dimensional
lattices becomes computationally intractable to optimally solve. Despite their
NP-hardness, we prove that efficient cycle-following based algorithms remain
asymptotically optimal for 2D fully- and partially-labeled settings, in
expectation, using the interesting fact that random permutations induce only a
small number of cycles. We further improve these algorithms to provide
1.x-optimality when the number of items is small. Simulation studies
corroborate the effectiveness of our algorithms.

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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci