In this note we describe efficient algorithms for generating tests that cover a, prescribed set, of combinations of a software system's input parameters. Our methods for obtaining uniform t-wise coverage are based on repeatedly coloring the vertices of a graph such that the vertices in each t-subset have different colors in at least one of the colorings. The resulting algorithm is compared to other known algorithms for uniform coverage, a greedy algorithm and a randomized algorithm, in particular. The size of its output test suite is then related to a new lower bound that we obtain on the minimal size of a test suite.
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