Abstract We consider supercritical site percolation on the $d$ -dimensional hypercube $Q^d$ . show that typically all components in percolated hypercube, besides giant, are of size $O(d)$ This resolves a conjecture Bollobás, Kohayakawa, and Łuczak from 1994.

This paper describes parallel algorithms for the following operations on qua.dtreesboolean operations (union, intersection, complement), collapsing a quadtree, and neighbor finding in an image represented by a quadtree. The architecture assumed in this paper is a. hypercube with one processing element (PE) per hypercube node. We assume that the architecture is SIMD, i.e., all PEs work under the...

A partial cube is a graph that can be isometrically embedded into a hypercube. In other words, a partial cube is a subgraph of a hypercube that preserves distances the distance between any two vertices in the subgraph is the same as the distance between those vertices in the hypercube. Partial cubes were first introduced by Graham and Pollak (Graham & Pollak, 1971) as a model for communication ...

Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms become more challenging. A method is proposed for performing exact hypercube convolution in sub-quadratic time. The method outperforms FFTPACK, called via numpy, and FFTW, called via pyfftw...