Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Greedy Clustering and Distance Selection for Graph Metrics   $\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important
problems defined on finite metric spaces, and provide efficient new algorithms
and approximation schemes for these problems on inputs given as graph shortest
path metrics or high-dimensional Euclidean metrics. The first of these problems
is the greedy permutation (or farthest-first traversal) of a finite metric
space: a permutation of the points of the space in which each point is as far
as possible from all previous points. We describe randomized algorithms to find
$(1+\eps)$-approximate greedy permutations of any graph with $n$ vertices and
$m$ edges in expected time $O(\eps^{-1}(m+n)\log n\log(n/\eps))$, and to find
$(1+\eps)$-approximate greedy permutations of points in high-dimensional
Euclidean spaces in expected time $O(\eps^{-2} n^{1+1/(1+\eps)^2 + o(1)})$.
Additionally we describe a deterministic algorithm to find exact greedy
permutations of any graph with $n$ vertices and treewidth $O(1)$ in worst-case
time $O(n^{3/2}\log^{O(1)} n)$. The second of the two problems we consider is
distance selection: given $k \in [ \binom{n}{2} ]$, we are interested in
computing the $k$th smallest distance in the given metric space. We show that
for planar graph metrics one can approximate this distance, up to a constant
factor, in near linear time.

30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an