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Content Provider | Directory of Open Access Journals (DOAJ) |
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Author | Hyunh Thi Thanh Binh Keiichi Kaneko Son Van Nguyen |
Abstract | The pairwise disjoint paths problem is to construct c disjoint paths $s_{i}$ → $d_{i}$ (1 ≤ i ≤ c) between given pairs of nodes $(s_{i}$, $d_{i}$) (1 ≤ i ≤ c) in a graph whose connectivity is no less than 2c. It is a major problem for interconnection networks, together with the node-to-node disjoint paths problem, the node-to-set disjoint paths problem, and the set-to-set disjoint paths problem. In this paper, we propose an algorithm that solves this problem for a torus. In a previous work, Bossard and Kaneko have developed an algorithm that constructs disjoint paths between c pairs of nodes in a k-ary n-dimensional torus, where c ≤ n. The time complexity of their algorithm is $O(c^{4}$n+kcn), and the maximum path length is [k/2jn+2k(c-1). However, the algorithm proposed in this paper achieves a time complexity of $O(c^{3}$n+kcn), and its maximum path length is [k/2jn + ([3k/21 - 2)(c - 1), which are both improvements over the previous algorithm. We also conducted an evaluation experiment to show that the average path lengths are proportional to k if n is fixed, and ton if k is fixed. The theoretical maximum path lengths were not attained by the paths constructed by our algorithm, and the average execution time was proportional to k if n is fixed, and to $n^{2}$ if k is fixed. Additional experimental results show that, compared to the previous algorithm by Bossard and Kaneko, our algorithm achieves a better performance with respect to the maximum path lengths, but both algorithms achieve a similar level of performance with respect to the average maximum path lengths. Also, it is shown that the average execution time of our algorithm is about $O(n^{2}$), which is better than the average execution time of the previous algorithm $O(n^{3}$) in the experimental framework. |
e-ISSN | 21693536 |
DOI | 10.1109/ACCESS.2020.3032684 |
Journal | IEEE Access |
Volume Number | 8 |
Language | English |
Publisher | IEEE |
Publisher Date | 2020-01-01 |
Publisher Place | United States |
Access Restriction | Open |
Subject Keyword | Electrical Engineering. Electronics. Nuclear Engineering Fault Tolerant Systems Multiprocessor Interconnection Networks Network Topology Parallel Processing Supercomputers |
Content Type | Text |
Resource Type | Article |
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