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One of the routing paradigms on interconnection networks is as follows: given a source node and \(m\) destination nodes, find disjoint paths from the source to the destination nodes. If we impose the condition that these paths be the shortest ones, this problem becomes harder and more interesting because such shortest and disjoint paths do not always exist. This problem has been studied previously for \(Q_n\), the hypercube of dimension \(n\), when \(m = n\) and a necessary and sufficient condition has been found for these paths to exist. In this paper, we review the previous work for the hypercube and then consider the problem in the more general case for arbitrary \(m\), where \(1 \leq m \leq 2^n – 1\), in an \(n\)-cube by designing routing algorithms that always find disjoint and shortest paths for a maximum subset of the destination nodes for which such paths exist. The size of such a set is no more than \(n\), the degree of the \(Q_n\).