Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. We consider the problem of computing rankings for Katz centrality. In particular, we propose upper and lower bounds on the Katz score of a given node. While previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings, we construct an algorithm that iteratively improves those upper and lower bounds until a correct Katz ranking is obtained. For a certain class of inputs, this yields an optimal algorithm for Katz ranking computation. Furthermore, Experiments demonstrate that our algorithm outperforms both numerical approaches and heuristics with speedups between 1.5x and 3.5x, depending on the desired quality guarantees. Specifically, we provide efficient parallel CPU and GPU implementations of the algorithms that enable near real-time Katz centrality computation for graphs with hundreds of millions of nodes in fractions of seconds.