The properties and t/s-diagnosability of k-ary n-cube networks

Xie, Yucheng; Liang, Jiarong; Yin, Wen; Li, Changzhen

doi:10.1007/s11227-021-04155-y

Cited by 8 publications

(2 citation statements)

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“…If k = 2, then the structure is an n-hypercube, where nodes are located right on each corner. However, if k > 2, then nodes are equally distributed along the whole shape [16].…”

Section: K-ary N-cubesmentioning

confidence: 99%

“…From that point on, taking a random node d, whose value related to a given dimension i is d i , then the node attached to the left in that dimension i is assigned to the predecessor modulo k of the value d i , whilst the node attached to the right is assigned to the successor modulo k of the value d i , as expressed in (15). However, if the binary alphabet is employed, then such an expression gets simplified because there are only two neighbors in each dimension, as in (16).…”

Section: K-ary N-cubesmentioning

confidence: 99%

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Arithmetic modeling of k-ary n-cubes and toroidal k-ary grids

Roig,

Alcaraz,

Gilly

et al. 2024

J. Phys.: Conf. Ser.

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The use of toroidal topologies offers many advantages in the computing field when it comes to both pattern spotting and path finding strategies. The former is covered by de Bruijn shapes, which permit to uniquely locate a single pattern throughout the shape. However, the latter is mainly carried out by k-ary n-cubes, which label node identifiers in a sequential order according to rows, columns, layers, and so on. This scheme facilitates the movement among nodes by just applying arithmetic operations, such as integer divisions and arithmetic modulo n. On the othe hand, toroidal k-ary grids are an alternative available in some specific cases, where determined patterns appear in all dimensions of each node, thus allowing to use those patterns to dictate paths to move among nodes. In this paper, the arithmetic bases of both path finding strategies have been presented and some pseudocode algorithms have been designed.

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“…If k = 2, then the structure is an n-hypercube, where nodes are located right on each corner. However, if k > 2, then nodes are equally distributed along the whole shape [16].…”

Section: K-ary N-cubesmentioning

confidence: 99%

Section: K-ary N-cubesmentioning

confidence: 99%