On the construction of all shortest vertex-disjoint paths in Cayley graphs of abelian groups

Low time complexity algorithms for path computation in Cayley Graphs

“…We show that our algorithm for disjoint paths outperforms the topology-agnostic solution [4]. Moreover, we show that for many families of CG used as model of communication networks, our algorithm for K-shortest disjoint paths stays competitive with respect to the algorithms presented in [12,18].…”

“…The algorithms proposed in this paper extend the work of [1]. In contrast to the algorithms presented in [12,14,16], our algorithms are topology-agnostic and have no constraints on the size of the computed paths. In addition, we present an algorithm for computing the shortest path avoiding a set of nodes and edges, which is useful in the design of fault-tolerant routing schemes.…”

“…This algorithm runs in time O(K∆ 3 ) if the computed paths have length less than 2∆ + 16. An algorithm for computing the K-shortest vertex-disjoint paths in CG of abelian groups, which includes several families of CG such as hypercubes and buble-sort graphs, is presented in [12]. This algorithm has time complexity in O(K∆D).…”

“…However, routing schemes with low space and time complexity can be designed taking advantage of the vertex-transitive property of CG [9]. Recent proposals in this direction include algorithms for path computation in specific families of CG [12,14]. To the best of our knowledge, there is no topology-agnostic algorithms for path computation in CG.…”

On the construction of all shortest node-disjoint paths in star networks

“…Recently, all shortest disjoint paths from one source node/vertex to other (not necessarily distinct) target nodes/ vertices have been constructed in hypercubes [11], tori [9], and the Cayley graphs of abelian groups [10]. In this paper, we study the problem of constructing m disjoint shortest paths from one source node to other m (not necessarily distinct) target nodes in an n-star, where m ≤ n − 1 and n ≥ 3.…”