Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Polynomial Time Algorithm for Almost Optimal Vertex Fault Tolerant
  Spanners   We present the first polynomial time algorithm for the f vertex fault
tolerant spanner problem, which achieves almost optimal spanner size. Our
algorithm for constructing f vertex fault tolerant spanner takes $O(k\cdot
n\cdot m^2 \cdot W)$ time, where W is the maximum edge weight, and constructs a
spanner of size $O(n^{1+1/k}f^{1-1/k}\cdot (\log n)^{1-1/k})$. Our spanner has
almost optimal size and is at most a $\log n$ factor away from the upper bound
on the worst-case size. Prior to this work, no other polynomial time algorithm
was known for constructing f vertex fault tolerant spanner with optimal size.
  Our algorithm is based on first greedily constructing a hitting set for the
collection of paths of weight at most $k \cdot w(u,v)$ between the endpoints u
and v of an edge (u,v) and then using this set to decide whether the edge (u,v)
needs to be added to the growing spanner.

21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics