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

• We investigate the problem of constructing a dual-CIST on bicubes B Q n. • A newly generic adjustment scheme can reduce the diameter of dual-CIST. • The diameter of the constructed dual-CIST of B Q n is 2 n − 2 for n ⩾ 5 odd. • The diameter of the constructed dual-CIST of B Q n is 2 n − 3 for n ⩾ 6 even. • As a by-product, a folded hypercube F Q n admits a dual-CIST with diameter 2 n − 2. Recently, an innovative hypercube-variant network called bicube, denoted as B Q n , 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 2 n − 1 on B Q n. 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 T i for i = 1 , 2 we constructed for B Q n are as follows: diam (T i) = { 7 if n = 4 ; 2 n − 2 if n ⩾ 5 and n is odd ; 2 n − 3 if n ⩾ 6 and n is even. [ABSTRACT FROM AUTHOR]