Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reasoning about Cardinal Directions between Extended Objects: The
  Hardness Result   The cardinal direction calculus (CDC) proposed by Goyal and Egenhofer is a
very expressive qualitative calculus for directional information of extended
objects. Early work has shown that consistency checking of complete networks of
basic CDC constraints is tractable while reasoning with the CDC in general is
NP-hard. This paper shows, however, if allowing some constraints unspecified,
then consistency checking of possibly incomplete networks of basic CDC
constraints is already intractable. This draws a sharp boundary between the
tractable and intractable subclasses of the CDC. The result is achieved by a
reduction from the well-known 3-SAT problem.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol