Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic Analysis of RRT Trees   This thesis presents analysis of the properties and run-time of the
Rapidly-exploring Random Tree (RRT) algorithm. It is shown that the time for
the RRT with stepsize $\epsilon$ to grow close to every point in the
$d$-dimensional unit cube is $\Theta\left(\frac1{\epsilon^d} \log
\left(\frac1\epsilon\right)\right)$. Also, the time it takes for the tree to
reach a region of positive probability is $O\left(\epsilon^{-\frac32}\right)$.
Finally, a relationship is shown to the Nearest Neighbour Tree (NNT). This
relationship shows that the total Euclidean path length after $n$ steps is
$O(\sqrt n)$ and the expected height of the tree is bounded above by $(e +
o(1)) \log n$.

26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn