Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spanners in randomly weighted graphs: independent edge lengths   Given a connected graph $G=(V,E)$ and a length function $\ell:E\to {\mathbb
R}$ we let $d_{v,w}$ denote the shortest distance between vertex $v$ and vertex
$w$. A $t$-spanner is a subset $E'\subseteq E$ such that if $d'_{v,w}$ denotes
shortest distances in the subgraph $G'=(V,E')$ then $d'_{v,w}\leq t d_{v,w}$
for all $v,w\in V$. We show that for a large class of graphs with suitable
degree and expansion properties with independent exponential mean one edge
lengths, there is w.h.p.~a 1-spanner that uses $\approx \frac12n\log n$ edges
and that this is best possible. In particular, our result applies to the random
graphs $G_{n,p}$ for $np\gg \log n$.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas