Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological complexity and efficiency of motion planning algorithms   We introduce a variant of Farber's topological complexity, defined for smooth
compact orientable Riemannian manifolds, which takes into account only motion
planners with the lowest possible "average length" of the output paths. We
prove that it never differs from topological complexity by more than $1$, thus
showing that the latter invariant addresses the problem of the existence of
motion planners which are "efficient".

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an