Constructing dual-CISTs with short diameters using a generic adjustment scheme on bicubes

Abstract

Recently, an innovative hypercube-variant network called bicube, denoted as BQn, has been proposed to possess both short diameter and symmetry advantages. Unlike other existing hypercube-variant networks, they lose their symmetry in pursuit of short diameters. For solving the problems of fault-tolerant transmission and secure message distribution in a reliable network, one solution suggested a dual-CIST (two completely independent spanning trees) to design a multi-path routing (e.g., a recently proposed secure-protection routing). We can make the construction using the standard arrangement guideline (SAG) like the hypercubes to obtain a dual-CIST with a diameter of 2n−1 on BQn. This paper proposes a newly generic adjustment scheme (GAS) for reducing the diameter of the dual-CIST under this construction. As a result, the diameter of Ti for i=1,2 we constructed for BQn are as follows:diam(Ti)={7if n=4;2n−2if n⩾5 and nis odd;2n−3if n⩾6 and nis even.