Embedding of Hypercubes into l-Sibling Trees

Abstract

The hypercube is one of the most popular interconnection networks due to its structural regularity, potential for parallel computation of various algorithms, and the high degree of fault tolerance. In this paper, we introduce a tree called l-sibling trees and the main results obtained in this paper are: (1) For r ≥ 1, the minimum wirelength of embedding r-dimensional hypercube into r-dimensional l-sibling tree. (2) For r ≥ 1, embedding of r-dimensional extended l-sibling tree into caterpillar with minimum dilation. (3) Based on the proof of (1), we provide an O(r)-linear time algorithm to compute the minimum wirelength of embedding r-dimensional hypercube into r-dimensional l-sibling tree.