Spanning Trees and Communication Primitives on Hypercubes

We will present optimal or nearly optimal algorithms for four communication problems on hypercubes: (i) one-to-all broadcasting, (ii) one-to-all personalized communication (iii) all-to-all broadcasting, and (iv) all-to-all personalized communication. Specifically, spanning trees such as binomial trees, rotated binomial trees, edge-disjoint spanning trees and balanced trees will be defined and their properties be analyzed. Then, algorithms based on these spanning trees will be described. Also, some recent implementation on the Intel iPSC/2 and iPSC/860 will be included. At the end, we will also give a brief survey on many recent related results by us and others.

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