A Note on Valid Inequalities for PageRank Optimization with Edge Selection Constraints

TL;DR

This paper develops polynomial-time valid inequalities to address NP-hard PageRank optimization problems with edge selection constraints, building on prior theoretical insights about their complexity.

Contribution

It introduces a method to generate valid inequalities in polynomial time for NP-hard PageRank optimization with edge constraints, enhancing solution approaches.

Findings

Valid inequalities can be generated efficiently for constrained PageRank optimization.

The approach leverages theoretical NP-hardness results to improve practical solving.

Polynomial-time inequalities aid in tackling complex edge selection problems.

Abstract

Cs\'{a}ji, Jungers, and Blondel prove that while a PageRank optimization problem with edge selection constraints is NP-hard, it can be solved optimally in polynomial time for the unconstrained case. This theoretical result is accompanied by several observations, which we leverage to develop valid inequalities in polynomial time for this class of NP-hard problems.