Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

摘要

Independent spanning trees (ISTs) have increasing applications in fault-tolerance, bandwidth, and security. In this paper, we study the problem of parallel construction of ISTs on crossed cubes. We first propose the definitions of dimension-adjacent walk and dimension-adjacent tree along with a dimension property of crossed cubes. Then, we consider the parallel construction of ISTs on crossed cubes. We show that there exist n general dimension-adjacent trees which are independent of the addresses of vertices in the n-dimensional crossed cube CQ_n. Based on n dimension-adjacent trees and an arbitrary root vertex, a parallel algorithm with the time complexity O(2~n) is proposed to construct n ISTs on CQ_n, where n≥ 1.