Playing tetris on meshes and multi-dimensional Shearsort
Shearsort is a classical sorting algorithm working in rounds on 2-dimensional meshes of processors. Its elementary and elegant runtime analysis can be found in various textbooks. There is a straightforward generalization of Shearsort to multi-dimensional meshes. As experiments turn out, it works fast. However, no method has yet been shown strong enough to provide a tight analysis of this algorithm. In this paper, we present an analysis of the 3-dimensional case and show that on the l x l x l-mesh, it suffices to perform 21ogl+ 10 rounds while 2logl+1 rounds are necessary. Moreover, tools for analyzing multi-dimensional Shearsort are provided.
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