Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Map Matching with Simplicity Constraints   We study a map matching problem, the task of finding in an embedded graph a
path that has low distance to a given curve in R^2. The Fr\'echet distance is a
common measure for this problem. Efficient methods exist to compute the best
path according to this measure. However, these methods cannot guarantee that
the result is simple (i.e. it does not intersect itself) even if the given
curve is simple. In this paper, we prove that it is in fact NP-complete to
determine the existence a simple cycle in a planar straight-line embedding of a
graph that has at most a given Fr\'echet distance to a given simple closed
curve. We also consider the implications of our proof on some variants of the
problem.

9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat