Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional Reliability in Uncertain Graphs   Network reliability is a well-studied problem that requires to measure the
probability that a target node is reachable from a source node in a
probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned
a probability of existence. Many approaches and problem variants have been
considered in the literature, all assuming that edge-existence probabilities
are fixed. Nevertheless, in real-world graphs, edge probabilities typically
depend on external conditions. In metabolic networks a protein can be converted
into another protein with some probability depending on the presence of certain
enzymes. In social influence networks the probability that a tweet of some user
will be re-tweeted by her followers depends on whether the tweet contains
specific hashtags. In transportation networks the probability that a network
segment will work properly or not might depend on external conditions such as
weather or time of the day. In this paper we overcome this limitation and focus
on conditional reliability, that is assessing reliability when edge-existence
probabilities depend on a set of conditions. In particular, we study the
problem of determining the k conditions that maximize the reliability between
two nodes. We deeply characterize our problem and show that, even employing
polynomial-time reliability-estimation methods, it is NP-hard, does not admit
any PTAS, and the underlying objective function is non-submodular. We then
devise a practical method that targets both accuracy and efficiency. We also
study natural generalizations of the problem with multiple source and target
nodes. An extensive empirical evaluation on several large, real-life graphs
demonstrates effectiveness and scalability of the proposed methods.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas