Optimizing Node Discovery on Networks: Problem Definitions, Fast Algorithms, and Observations
Abstract
Many people dream to become famous, YouTube video makers also wish their videos to have a large audience, and product retailers always hope to expose their products to customers as many as possible. Do these seemingly different phenomena 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 a target node wants to be discovered easily by the other nodes in the network. In this work, we explicitly define a node's discoverability in a network, and formulate a general node discoverability optimization problem, where the goal is to create a budgeted set of incoming edges to the target node so as to optimize the target node's discoverability in the network. Although the optimization problem is proven to be NPhard, we find that the defined discoverability measures have good properties that enable us to use a greedy algorithm to find provably nearoptimal solutions. The computational complexity of 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 large networks, we propose an estimationandrefinement approach, that provides a good tradeoff between estimation accuracy and computational efficiency. Experiments conducted on realworld networks demonstrate that our method is thousands of times faster than an exact method using dynamic programming, thereby allowing us to solve the node discoverability optimization problem on large networks.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.04307
 Bibcode:
 2017arXiv170304307Z
 Keywords:

 Computer Science  Social and Information Networks
 EPrint:
 45 pages, 13 figures