Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data
  Structures for Unweighted Graph   Let $G=(V,E)$ be any undirected graph on $V$ vertices and $E$ edges. A path
$\textbf{P}$ between any two vertices $u,v\in V$ is said to be $t$-approximate
shortest path if its length is at most $t$ times the length of the shortest
path between $u$ and $v$. We consider the problem of building a compact data
structure for a given graph $G$ which is capable of answering the following
query for any $u,v,z\in V$ and $t>1$:
  Report $t$-approximate shortest path between $u$ and $v$ when vertex $z$
fails
  We present data structures for the single source as well all-pairs versions
of this problem. Our data structures guarantee optimal query time. Most
impressive feature of our data structures is that their size {\em nearly} match
the size of their best static counterparts.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph