Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Decomposition-Based Approach to Reasoning about Free Space
  Path-Connectivity for Rigid Objects in 2D   In this paper, we compute a conservative approximation of the path-connected
components of the free space of a rigid object in a 2D workspace in order to
solve two closely related problems: to determine whether there exists a
collision-free path between two given configurations, and to verify whether an
object can escape arbitrarily far from its initial configuration -- i.e.,
whether the object is caged. Furthermore, we consider two quantitative
characteristics of the free space: the volume of path-connected components and
the width of narrow passages. To address these problems, we decompose the
configuration space into a set of two-dimensional slices, approximate them as
two-dimensional alpha-complexes, and then study the relations between them.
This significantly reduces the computational complexity compared to a direct
approximation of the free space. We implement our algorithm and run experiments
in a three-dimensional configuration space of a simple object showing runtime
of less than 2 seconds.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin