Path Embeddings with Prescribed Edge in the Balanced Hypercube Network

Dan Chen,Gaofeng Zhang,Zhongzhou Lu,Zebang Shen,Chong Chen,Qingguo Zhou

doi:10.3390/sym9060079

Abstract

The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition V 0 ∪ V 1 x ∈ V 0 y ∈ V 1 . It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge e in the balanced hypercube, there exists a Hamiltonian path between any two vertices x and y in different partite sets passing through e with e ≠ x y . This result improves some known results.

Highlights

Interconnection networks play an essential role in the performance of parallel and distributed systems
In the event of practice, large multi-processor systems can be adopted as tools to address complex management and big data problems. It is well-known that an interconnection network is generally modeled by an undirected graph, in which processors are represented by vertices and communication links between them are represented by edges
It has been proved that the diameter of an odd-dimensional balanced hypercube BHn is 2n − 1 [10], which is smaller than that of the hypercube Q2n

Summary

Introduction

Interconnection networks play an essential role in the performance of parallel and distributed systems. In the event of practice, large multi-processor systems can be adopted as tools to address complex management and big data problems It is well-known that an interconnection network is generally modeled by an undirected graph, in which processors are represented by vertices and communication links between them are represented by edges. The balanced hypercube possesses some desirable properties that the hypercube does not have, so it is interesting to explore other favorable properties that the balanced hypercube may have Since parallel applications such as image and signal processing are originally designed on array and ring architectures, it is important to have path and cycle embeddings in a network.

Preliminaries

Main Results

Conclusions