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原文摘要

PageRank is widely used to quantify the importance of nodes in directed networks. In applications such as recommendation systems, it is increasingly important that the PageRank distribution provides a fair representation of node exposure. This motivates the problem of making minimal changes to a graph so that the PageRank values of a given set of target nodes $T$ match a desired vector $\boldsymbol{t}$. In this paper, we study this problem under an edge-addition budget $B$, where exactly $B$ edges may be added to the graph. We show that deciding whether a multiset of exactly $B$ added edges can make the target nodes attain their desired absolute PageRank scores is NP-complete. After this, we define the $\ell_1$ Target PageRank problem in which we seek to minimize the $\ell_1$ distance between the target vector and resultant vector. We show that this optimization problem admits no polynomial-time multiplicative constant-factor approximation unless $P=NP$. Motivated by these hardness results, we propose two greedy heuristics for approaching the target PageRank vector. We additionally propose a Random Walk Hungarian (RWH) heuristic that addresses the addition of edges between dissimilar nodes by incorporating a penalty for such edges. Finally, we evaluate the proposed heuristics on several real-world and synthetic datasets and compare their performance in terms of PageRank accuracy, computational efficiency, and the relevance of the added edges.