Determining relationships such as functional or inclusion dependencies within and across databases is important for many applications in information integration. When such information is not available as explicit meta data, it is possible to discover potential dependencies from the source database extents. However, the complexity of such discovery problems is typically exponential in the number of attributes. We have developed an algorithm for the discovery of inclusion dependencies across high-dimensional relations in the order of 100 attributes. This algorithm is the first to efficiently solve the inclusion-dependency discovery problem. This is achieved by mapping it into a progressive series of clique-finding problems in k-uniform hypergraphs and solving those. Extensive experimental studies confirm the algorithm's efficiency on a variety of real-world data sets.