Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When Crossings Count - Approximating the Minimum Spanning Tree   In the first part of the paper, we present an (1+\mu)-approximation algorithm
to the minimum-spanning tree of points in a planar arrangement of lines, where
the metric is the number of crossings between the spanning tree and the lines.
The expected running time is O((n/\mu^5) alpha^3(n) log^5 n), where \mu > 0 is
a prescribed constant.
  In the second part of our paper, we show how to embed such a crossing metric,
into high-dimensions, so that the distances are preserved. As a result, we can
deploy a large collection of subquadratic approximations algorithms \cite
im-anntr-98,giv-rahdg-99 for problems involving points with the crossing metric
as a distance function. Applications include matching, clustering,
nearest-neighbor, and furthest-neighbor.

2
The categories of this paper are: math
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin