Optimizing node discovery on networks: Problem definitions, fast algorithms, and observations

We study a general node discoverability optimization problem on networks, where the goal is to create a few edges to a target node so that the target node can be easily discovered by the other nodes in the network. For instance, a jobseeker may want to connect with some members in LinkedIn so that recruiters can easily find him. We first propose two definitions of node discoverability. Then, we prove that the node discoverability optimization problem is NP-hard. We show that a greedy algorithm can be used to find near-optimal solutions. To scale up the algorithm on large networks, we design three methods: (1) an exact method based on dynamic programming, which is accurate but computationally inefficient; (2) an estimation method based on the framework of random walk, which is efficient but may be inaccurate; (3) an estimation-and-refinement method, which combines the previous two methods and we show that it is both accurate and efficient. Experiments conducted on real networks demonstrate that the estimation-and-refinement method can provide a good trade-off between solution accuracy and computational efficiency, and achieve speedup of up to three orders of magnitude over the exact method.