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This paper presents a constant slow-down, optimal and locally normal simulation for basic reconfigurable meshes on hypercubes, if the log-time delay model for broadcasting is assumed. Such a simulation algorithm is based on: (i) an O(log B) time algorithm for the segmented scan problem on a (2n - 1)-node toroidal X-tree, where B is the size of the longest segment; this algorithm is time optimal; (ii) a constant slow-down optimal and locally normal simulation algorithm for basic reconfigurable meshes on the mesh of toroidal X-trees; and (iii) a constant slow-down optimal simulation of locally normal algorithms for meshes of toroidal X-trees on the hypercube. |
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