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Many people dream to become famous, YouTube video makers also wish theirvideos to have a large audience, and product retailers always hope to exposetheir products to customers as many as possible. Do these seemingly differentphenomena share a common structure? We find that fame, popularity, or exposure,could be modeled as a node's discoverability on some properly defined network,and all of the previously mentioned phenomena can be commonly stated as atarget node wants to be discovered easily by the other nodes in the network. Inthis work, we explicitly define a node's discoverability in a network, andformulate a general node discoverability optimization problem, where the goalis to create a budgeted set of incoming edges to the target node so as tooptimize the target node's discoverability in the network. Although theoptimization problem is proven to be NP-hard, we find that the defineddiscoverability measures have good properties that enable us to use a greedyalgorithm to find provably near-optimal solutions. The computational complexityof a greedy algorithm is dominated by the time cost of an oracle call, i.e.,calculating the marginal gain of a node. To scale up the oracle call over largenetworks, we propose an estimation-and-refinement approach, that provides agood trade-off between estimation accuracy and computational efficiency.Experiments conducted on real-world networks demonstrate that our method isthousands of times faster than an exact method using dynamic programming,thereby allowing us to solve the node discoverability optimization problem onlarge networks.

Optimizing Node Discovery on Networks: Problem Definitions, Fast Algorithms, and Observations