Abstract
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 (, ), the proposed algorithm connects c () vertex pairs with mutually vertex-disjoint paths of lengths at most , and the worst-case time complexity of the algorithm is . Finally, empirical evaluation of the proposed algorithm is conducted in order to inspect its practical behavior.
Highlights
Since the development of parallel supercomputers, the number of included processors has been continuously rising
Hypercubes [1] were a popular topology for the interconnection network of massively parallel systems in the eighties
For instance, the iPSC supercomputer series, with the iPSC/1 device connecting 32 to 128 cores: the iPSC/d5 is based on a five-dimensional hypercube, connecting 25 = 32 cores; the iPSC/6 is based on a six-dimensional hypercube, connecting 64 cores, and the iPSC/d7 128 cores
Summary
Since the development of parallel supercomputers, the number of included processors has been continuously rising. The torus pairwise disjoint-path routing problem is addressed This critical data communication problem consists of the selection of mutually vertex-disjoint paths between several vertex pairs. A node-to-set disjoint-path routing algorithm in a torus has been described in Reference [19], with paths of lengths at most nbk/2c + 1, and a worst-case time complexity of O(k3 ). A torus set-to-set disjoint-path routing algorithm has been given in Reference [20], with paths of lengths at most 2(k + 1)n, and a worst-case time complexity of O(kn3 + n3 log n). In an n-dimensional k-ary torus, given c (c ≤ n) vertex pairs, the algorithm proposed here selects c mutually vertex-disjoint paths of lengths at most 2k(c − 1) + nbk/2c with a worst-case time complexity of O(nc ).
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