Background Double loop networks (DLN, for simplicity) G (n; h), where n is the number of its
nodes and 1 and h are its steps, are important interconnection networks. Some optimal
routing algorithms for G (n; h) have been proposed, their time complexity is at least O (n). In
this paper, DLN with restricted steps are considered. It is proved that if the step h satisfies a
certain inequality, then the formula for its diameter is given, and the constant time optimal
routing is obtained, precisely, at most 6 arithmetic operations or comparisons are needed to …