PageRank Optimization by Edge Selection

TL;DR

This paper presents a polynomial-time method for maximizing a node’s PageRank by selecting edges, using linear programming and greedy algorithms, while also identifying NP-hardness under certain constraints.

Contribution

It introduces a polynomial-time approach to optimize PageRank through edge selection, including linear programming and greedy algorithms, and proves NP-hardness with mutually exclusive edge pairs.

Findings

Optimal solution found via linear programming

Greedy algorithm provides an efficient approximation

NP-hardness established for specific edge constraints

Abstract

The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at the node by an infinite random walk. We consider the problem of maximizing the PageRank of a node by selecting some of the edges from a set of edges that are under our control. By applying results from Markov decision theory, we show that an optimal solution to this problem can be found in polynomial time. Our core solution results in a linear programming formulation, but we also provide an alternative greedy algorithm, a variant of policy iteration, which runs in polynomial time, as well. Finally, we show that, under the slight modification for which we are given mutually exclusive pairs of edges, the problem of PageRank optimization becomes NP-hard.