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Modern supercomputers include hundreds of thousands of processors and they are thus massively parallel systems. The interconnection network of a system is in charge of mutually connecting these processors. Recently, the torus has become a very popular interconnection network topology. For example, the Fujitsu K, IBM Blue Gene/L, IBM Blue Gene/P, and Cray Titan supercomputers all rely on this topology. The pairwise disjoint-path routing problem in a torus network is addressed in this paper. This fundamental problem consists of the selection of mutually vertex disjoint paths between given vertex pairs. Proposing a solution to this problem has critical implications, such as increased system dependability and more efficient data transfers, and provides concrete implementation of green and sustainable computing as well as security, privacy, and trust, for instance, for the Internet of Things (IoT). Then, the correctness and complexities of the proposed routing algorithm are formally established. Precisely, in an n-dimensional k-ary torus (n

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Numerous TOP500 supercomputers are based on a torus interconnection network. The torus topology is effectively one of the most popular interconnection networks for massively parallel systems due to its interesting topological properties such as symmetry and simplicity. For instance, the world-famous supercomputers Fujitsu K, IBM Blue Gene/L, IBM Blue Gene/P and Cray XT3 are all torus-based. In this paper, we propose an algorithm that constructs 2n mutually node-disjoint paths from a set S of 2n source nodes to a set D of 2n destination nodes in an n-dimensional k-ary torus T n,k (n ≥ 1, k ≥ 3). This algorithm is then formally evaluated. We have proved that the paths selected by the proposed algorithm have lengths at most 2(k + 1)n and can be obtained with a time complexity of O(kn 3 + n 3 log n).