Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An $O(\log n)$-approximation for the Set Cover Problem with Set
  Ownership   In highly distributed Internet measurement systems distributed agents
periodically measure the Internet using a tool called {\tt traceroute}, which
discovers a path in the network graph. Each agent performs many traceroute
measurement to a set of destinations in the network, and thus reveals a portion
of the Internet graph as it is seen from the agent locations. In every period
we need to check whether previously discovered edges still exist in this
period, a process termed {\em validation}. For this end we maintain a database
of all the different measurements performed by each agent. Our aim is to be
able to {\em validate} the existence of all previously discovered edges in the
minimum possible time. In this work we formulate the validation problem as a
generalization of the well know set cover problem. We reduce the set cover
problem to the validation problem, thus proving that the validation problem is
${\cal NP}$-hard. We present a $O(\log n)$-approximation algorithm to the
validation problem, where $n$ in the number of edges that need to be validated.
We also show that unless ${\cal P = NP}$ the approximation ratio of the
validation problem is $\Omega(\log n)$.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat