Social media have a great potential to improve information dissemination in our society, yet, they have been held accountable for a number of undesirable effects, such as polarization and filter bubbles. It is thus important to understand these negative phenomena and develop methods to combat them. In this paper we propose a novel approach to address the problem of breaking filter bubbles in social media. We do so by aiming to maximize the diversity of the information exposed to connected social-media users. We formulate the problem of maximizing the diversity of exposure as a quadratic-knapsack problem. We show that the proposed diversity-maximization problem is inapproximable, and thus, we resort to polynomial non-approximable algorithms, inspired by solutions developed for the quadratic-knapsack problem, as well as scalable greedy heuristics. We complement our algorithms with instance-specific upper bounds, which are used to provide empirical approximation guarantees for the given problem instances. Our experimental evaluation shows that a proposed greedy algorithm followed by randomized local search is the algorithm of choice given its quality-vs.-efficiency trade-off.