Consider a d-dimensional closed ball B whose center coincides with that of the hypercube [0, 1]d. Pick radius in such way vertices are outside and midpoints its edges interior B. It is known that, when d ≥ 3, (d − 1)-dimensional volume H∩[0, 1]d, where H hyperplane ℝd tangent to B, largest possible if only orthogonal diagonal hypercube. shown here same holds 5 but required contain centers squar...

Parallel FFT data-flow graphs based on a Butterfly graph followed by a bit-reversal permutation are known, as are optimal-order embeddings of these flow-graphs onto meshes and hypercubes. Embeddings onto a 2D mesh require O(sqrtN) data transfer steps and O(logN) computation steps. Embeddings onto a hypercube require O(logN) data transfer steps and O(logN) computation steps. A similar FFT algori...

In this paper we present randomized algorithms for selection on the hypercube. We identify two variants of the hypercube namely, the sequential model and the parallel model. In the sequential model, any node at any time can handle only communication along a single incident edge, whereas in the parallel model a node can communicate along all its incident edges at the same time. We specify three ...

In this paper we present randomized algorithms for selection on the hypercube. We identify two variants of the hypercube namely, the sequential model and the parallel model. In the sequential model, any node at any time can handle only communication along a single incident edge, whereas in the parallel model a node can communicate along all its incident edges at the same time. We specify three ...