  Given a large network and a query node, finding its top-k similar nodes is a
primitive operation in many graph-based applications. Recently enhancing search
results with diversification have received much attention. In this paper, we
explore an novel problem of searching for top-k diversified similar nodes in
attributed networks, with the motivation that modeling diversification in an
attributed network should consider both the emergence of network links and the
attribute features of nodes such as user profile information. We formulate this
practical problem as two optimization problems: the Attributed Coverage
Diversification (ACD) problem and the r-Dissimilar Attributed Coverage
Diversification (r-DACD) problem. Based on the submodularity and the
monotonicity of ACD, we propose an efficient greedy algorithm achieving a tight
approximation guarantee of 1-1/e. Unlike the expension based methods only
considering nodes' neighborhood, ACD generalize the definition of
diversification to nodes' own features. To capture diversification in
topological structure of networks, the r-DACD problem introduce a dissimilarity
constraint. We refer to this problem as the Dissimilarity Constrained
Non-monotone Submodular Maximization (DCNSM) problem. We prove that there is no
constant-factor approximation for DCNSM, and also present an efficient greedy
algorithms achieving $1/\rho$ approximation, where $\rho\le\Delta$, $\Delta$ is
the maximum degree of its dissimilarity based graph. To the best of our
knowledge, it is the first approximation algorithm for the Submodular
Maximization problem with a distance constraint. The experimental results on
real-world attributed network datasets demonstrate the effectiveness of our
methods, and confirm that adding dissimilarity constraint can significantly
enhance the performance of diversification.
