Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fault-Tolerant Labeling and Compact Routing Schemes   The paper presents fault-tolerant (FT) labeling schemes for general graphs,
as well as, improved FT routing schemes. For a given $n$-vertex graph $G$ and a
bound $f$ on the number of faults, an $f$-FT connectivity labeling scheme is a
distributed data structure that assigns each of the graph edges and vertices a
short label, such that given the labels of the vertices $s$ and $t$, and at
most $f$ failing edges $F$, one can determine if $s$ and $t$ are connected in
$G \setminus F$. The primary complexity measure is the length of the individual
labels. Since their introduction by [Courcelle, Twigg, STACS '07], compact FT
labeling schemes have been devised only for a limited collection of graph
families. In this work, we fill in this gap by proposing two (independent) FT
connectivity labeling schemes for general graphs, with a nearly optimal label
length. This serves the basis for providing also FT approximate distance
labeling schemes, and ultimately also routing schemes. Our main results for an
$n$-vertex graph and a fault bound $f$ are:
  -- There is a randomized FT connectivity labeling scheme with a label length
of $O(f+\log n)$ bits, hence optimal for $f=O(\log n)$. This scheme is based on
the notion of cycle space sampling [Pritchard, Thurimella, TALG '11].
  -- There is a randomized FT connectivity labeling scheme with a label length
of $O(\log^3 n)$ bits (independent of the number of faults $f$). This scheme is
based on the notion of linear sketches of [Ahn et al., SODA '12].
  -- For $k\geq 1$, there is a randomized routing scheme that routes a message
from $s$ to $t$ in the presence of a set $F$ of faulty edges, with stretch
$O(|F|^2 k)$ and routing tables of size $\tilde{O}(f^3 n^{1/k})$.
  This significantly improves over the state-of-the-art bounds by [Chechik,
ICALP '11], providing the first scheme with sub-linear FT labeling and routing
schemes for general graphs.

10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat