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