Independent spanning trees in Eisenstein-Jacobi networks

Spanning trees are widely used in interconnection networks for routing, broadcasting, fault-tolerance, and securely delivering messages, as well as parallel and distributed computing. The problem of efficiently finding a maximal set of independent spanning trees (ISTs) is still open for arbitrary (general) interconnection topologies (graphs). The first contribution of this paper is presenting two efficient methods that solve the problem in Eisenstein-Jacobi (EJ) networks. The first constructs three Edge-Disjoint Node-Independent Spanning Trees (EDNISTs), whereas the second constructs six ISTs but not edge disjoint. Both constructions have time complexity O(n), where n is the number of nodes. The second contribution is providing a distributed fault-tolerant routing algorithm based on the constructed trees with time complexity O(1) and communication complexity O(|P|), where P is the routing path. The experimental results measure the maximum and the average of all maximum number of communication steps between the root node and all other nodes among all ISTs with the consideration of all possible faulty nodes. In addition, the comparison shows that the proposed method outperforms the state-of-the-art method in broadcasting in terms of node coverage in the presence of failures.