The computational complexity of link building

Abstract

We study the problem of adding k new links to a directed graph G(V, E) in order to maximize the minimum PageRank value for a given subset of the nodes. We show that this problem is NP-hard if k is part of the input. We present a simple and efficient randomized algorithm for the simple case where the objective is to compute one new link pointing to a given node t producing the maximum increase in the PageRank value for t. The algorithm computes an approximation of the PageRank value for t in G(V, E ∪ {(v, t)}) for all nodes v with a running time corresponding to a small and constant number of PageRank computations. © 2008 Springer-Verlag Berlin Heidelberg.