Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Particle-Based Assembly Using Precise Global Control   In micro- and nano-scale systems, particles can be moved by using an external
force like gravity or a magnetic field. In the presence of adhesive particles
that can attach to each other, the challenge is to decide whether a shape is
constructible. Previous work provides a class of shapes for which
constructibility can be decided efficiently, when particles move maximally into
the same direction induced by a global signal. In this paper we consider the
single step model, i.e., each particle moves one unit step into the given
direction. We prove that deciding constructibility is NP-complete for
three-dimensional shapes, and that a maximum constructible shape can be
approximated. The same approximation algorithm applies for 2D. We further
present linear-time algorithms to decide whether or not a tree-shape in 2D or
3D is constructible. Scaling a shape yields constructibility; in particular we
show that the $2$-scaled copy of every non-degenerate polyomino is
constructible. In the three-dimensional setting we show that the $3$-scaled
copy of every non-degenerate polycube is constructible.

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The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
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The categories of this paper are: math
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph