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d {\displaystyle d} -dimensional hypercube is a network topology for parallel computers with 2 d {\displaystyle 2^{d}} processing elements. The topology allows for an efficient implementation of some basic communication primitives such as Broadcast, All-Reduce, and Prefix sum. The processing elements are numbered 0 {\displaystyle 0} through 2 d − 1 {\displaystyle 2^{d}-1}. Each processing element is adjacent to processing elements whose numbers differ in one and only one bit. The algorithms described in this page utilize this structure efficiently.
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