Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Euclidean Steiner Trees   An approximate Steiner tree is a Steiner tree on a given set of terminals in
Euclidean space such that the angles at the Steiner points are within a
specified error e from 120 degrees.This notion arises in numerical
approximations of minimum Steiner trees (W. D. Smith, Algorithmica, 7 (1992),
137--177). We investigate the worst-case relative error of the length of an
approximate Steiner tree compared to the shortest tree with the same
topology.Rubinstein, Weng and Wormald (J. Global Optim. 35 (2006), 573--592)
conjectured that this relative error is at most linear in $e$, independent of
the number of terminals. We verify their conjecture for the two-dimensional
case as long as the error $e$ is sufficiently small in terms of the number of
terminals. We derive a lower bound linear in $e$ for the relative error in the
two-dimensional case when $e$ is sufficiently small in terms of the number of
terminals. We find improved estimates of the relative error for larger values
of $e$, and calculate exact values in the plane for three and four terminals.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ph