Ergodic Control and Polyhedral approaches to PageRank Optimization

TL;DR

This paper develops polynomial-time algorithms for optimizing web page link strategies to improve PageRank, using ergodic control and polyhedral methods, applicable to large web graphs with various constraints.

Contribution

It introduces a novel polyhedral approach to solve PageRank optimization problems efficiently, even with complex constraints and large networks.

Findings

Continuous and discrete problems are solvable in polynomial time.

Optimal strategies may include a 'master' page linking to all controlled pages.

Algorithms perform well on real web graph fragments.

Abstract

We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are obligatory links, facultative links and forbidden links. We show that the continuous problem, as well as its discrete variant when there are no constraints coupling different pages, can both be modeled by constrained Markov decision processes with ergodic reward, in which the webmaster determines the transition probabilities of websurfers. Although the number of actions turns out to be exponential, we show that an associated polytope of transition measures has a concise representation, from which we deduce that the continuous problem is solvable in polynomial time, and that the same is true for the discrete problem when there are no coupling constraints. We also provide efficient algorithms, adapted to very large networks. Then, we investigate the qualitative features of optimal outlink strategies, and identify in particular assumptions under which there exists a "master" page to which all controlled pages should point. We report numerical results on fragments of the real web graph.