A fault-tolerant routing strategy in hypercube multicomputers

Chiu, Ge-Ming; Wu, Shui-Pao

doi:10.1109/12.485379

Cited by 76 publications

(8 citation statements)

References 17 publications

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“…A nonfaulty node u is fully reachable with respect to Hamming distance h if every nonfaulty node which is distance h away from u is reachable (involving no faulty nodes) from u by a path of length h 4 . Simulation results show that their algorithm performs better than the one from Reference 2 in that a larger percentage of paths found are shortest paths.…”

Section: Previous Resultsmentioning

confidence: 99%

“…Fault-tolerant routing was studied by Chiu and Wu. 2 They have defined safe and unsafe nodes as follows. A nonfaulty node is unsafe if it is adjacent to at least two faulty nodes or more than two faulty or unsafe nodes.…”

Section: Previous Resultsmentioning

confidence: 99%

“…Therefore, 1 will be removed from the set N and we try number 2 as the second element. Here is the DP table for P = [1,2].…”

Section: Examplesmentioning

confidence: 99%

“…This can be used for optimization as discussed in Section 4.9. Finally the answer is P = [1,3,4,5,2] which is equal to the path [00000 − 10000 − 10100 − 10110 − 11101 − 11111] that is depicted in Figure 9.…”

Section: Examplesmentioning

confidence: 99%

“…However, it is worth pointing out that paths found by these routing algorithms are not necessarily the shortest. Among the very few routings aimed at finding shortest paths with the presence of faulty nodes are the work by Chiu and Wu, 2 Day et al, 3 and Kaneko and Ito 4 . They all approach the problem with the assumption that each node knows only the status of their neighbors and thus they propose a distributed algorithm whereas we assume that the status of all nodes is known for the source node to find the shortest path.…”

Section: Introductionmentioning

confidence: 99%

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An efficient shortest path routing on the hypercube with blocking/faulty nodes

Niasari

Qiu

2020

Concurrency and Computation

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We investigate fault-tolerant shortest path problem in the hypercube between two nodes where some nodes are faulty (or blocked) and thus cannot be used in routing.Previously, several similar problems were studied where proposed algorithms are distributed and local-information-based, that is, each node in the network knows only its neighbor's status (faulty or not) and they also look for optimal or near-optimal paths.There have been studies that established some sufficient conditions for these paths to exist. Since these conditions are only sufficient, there could be shortest paths that will be missed by these conditions. We study the problem under the assumption that for two given nodes, a source node s, a target node t, only s requires to have a global information of the network in order to find a shortest path to t, should it exist. A shortest path is defined as the Hamming distance between s and t. This problem can be solved by trivial algorithms. The first is to try all possible paths. In an n-dimensional hypercube with 2 n vertices, this method would cost at least n! time. Another method is to perform a standard shortest path finding algorithm, which would require at least 2 n time. A routing algorithm has been previously developed which is efficient in certain situations.However, in the worst case, its running time could be exponential in the hypercube dimension. We propose an efficient algorithm with running time of O(n 3 m 2 ), polynomial in n, the hypercube dimension, and m, number of blocking nodes. We gain our efficiency by reducing the routing problem to a permutation problem which can be solved using inclusion-exclusion principle. We finally use dynamic programming technique to optimally count the terms. With the proposed algorithm, not only can we find a shortest path, if such a path does exist, but we can also count all possible shortest paths.

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Section: Previous Resultsmentioning

confidence: 99%

Section: Previous Resultsmentioning

confidence: 99%

“…Therefore, 1 will be removed from the set N and we try number 2 as the second element. Here is the DP table for P = [1,2].…”

Section: Examplesmentioning

confidence: 99%