Embedding fault-free cycles in crossed cubes with conditional link faults

摘要

The crossed cube, which is a variation of the hypercube, possesses some properties that are superior to those of the hypercube. In this paper, we show that with the assumption of each node incident with at least two fault-free links, an n-dimensional crossed cube with up to 2n - 5 link faults can embed, with dilation one, fault-free cycles of lengths ranging from 4 to 2~n. The assumption is meaningful, for its occurrence probability is very close to 1, and the result is optimal with respect to the number of link faults tolerated. Consequently, it is very probable that algorithms executable on rings of lengths ranging from 4 to 2~n can be applied to an n-dimensional crossed cube with up to 2n - 5 link faults.