Multiple network embeddings into hypercubes

TL;DR: This paper proposes and analyzes a new interconnection network called bubblesort star graph, which is the merger of the bubblesort graph and the star graph and presents the deadlock-free wormhole routing algorithm for the proposed network.

TL;DR: The use of matrices for the representation of graph embedding in a hypercube is demonstrated, and it is shown that for any regular binary-reflected tree T, n copies of T can be simultaneously embedded in an n-cube with congestion = 2.

TL;DR: This work optimally embeds multiple graphs into a hypermesh by a labeling strategy that is applicable to the embeddings of other classes of graphs including mesh, torus, and hypercube.

TL;DR: The authors show the embeddings of various types of n- node incomplete binary trees into n-node or (n+1)-node composite hypercubes with dilation of at most 2 and present lower bound proofs showing optimality of the dilation.

TL;DR: This paper investigates simulations of tree machines; the fact that divide-and-conquer algorithms are programmed naturally on trees motivates the investigation, and constructs a universal bounded-degree network on N nodes for which every N node binary tree is a spanning tree.

TL;DR: This paper provides a novel and optimal embedding of a complete binary tree in which all but one tree edges are mapped onto adjacent processors on the hypercube, and the remaining edge is routed through an unused processor.

TL;DR: The main results in this paper demonstrate that there exist pairs of integers 〈E, D〉 such that any n-vertex rectangular grid can be embedded into a square grid having at most En vertices, in such a way that images in the square grid of vertices that are adjacent in the rectangular grid are at most distance D apart.

TL;DR: In this article, the authors present a method for transforming certain large networks into quotient networks that emulate those large networks with fewer processors, which result in no loss in execution efficiency and can be easily modified to execute on the quotient network.