Providing Concise Database Covers Instantly By Recursive Tile Sampling

Known pattern discovery algorithms for finding tilings (covers of 0/1-databases consisting of 1-rectangles) cannot be integrated in instant and interactive KD tools, because they do not satisfy at least one of two key requirements: a) to provide results within a short response time of only a few seconds and b) to return a concise set of patterns with only a few elements that nevertheless covers a large fraction of the input database. In this paper we present a novel randomized algorithm that works well under these requirements. It is based on the recursive application of a simple tile sample procedure that can be implemented efficiently using rejection sampling. While, as we analyse, the theoretical solution distribution can be weak in the worst case, the approach performs very well in practice and outperforms previous sampling as well as deterministic algorithms.