Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured Discrete Shape Approximation: Theoretical Complexity and
  Practical Algorithm   We consider the problem of approximating a two-dimensional shape contour (or
curve segment) using discrete assembly systems, which allow to build geometric
structures based on limited sets of node and edge types subject to edge length
and orientation restrictions. We show that already deciding feasibility of such
approximation problems is NP-hard, and remains intractable even for very simple
setups. We then devise an algorithmic framework that combines shape sampling
with exact cardinality-minimization to obtain good approximations using few
components. As a particular application and showcase example, we discuss
approximating shape contours using the classical Zometool construction kit and
provide promising computational results, demonstrating that our algorithm is
capable of obtaining good shape representations within reasonable time, in
spite of the problem's general intractability. We conclude the paper with an
outlook on possible extensions of the developed methodology, in particular
regarding 3D shape approximation tasks.

34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga