The Hausdorff Voronoi diagram of clusters of points in the plane is a generalization of Voronoi diagrams based on the Hausdorff distance function. Its combinatorial complexity is O(n+m), where n is the total number of points and m is the number of crossings between the input clusters (formula presented) the number of clusters is k. We present efficient algorithms to construct this diagram via the randomized incremental construction (RIC) framework For non-crossing clusters (m=0), our algorithm runs in expected (formula presented) time and deterministic O(n) space. For arbitrary clusters the algorithm runs in expected (formula presented) space. The two algorithms can be combined in a crossing-oblivious scheme within the same bounds. We show how to apply the RIC framework efficiently to handle non-standard characteristics of generalized Voronoi diagrams, including sites (and bisectors) of non-constant complexity, sites that are not enclosed in their Voronoi regions, empty Voronoi regions, and finally, disconnected bisectors and Voronoi regions. The diagram finds direct applications.