Full Binary Tree-Based Fixed Degree Graph Design and Parallel Algorithm

Interconnection network is a network that connects processors and is an important factor in determining the performance of a parallel processing system. One measure of interconnection network evaluation is network cost, defined as degree \ast diameter. The interconnection networks proposed so far can be classified into mesh, hypercube, and star graph types based on the number of nodes. The interconnection network Tree-baseGraph({TG}_{n}) proposed in this study is a graph based on a full binary tree with a fixed degree of three, and the node address is expressed using n binary numbers. In this study, routing algorithms, Hamiltonian cycle, node disjoint parallel path, etc. are analyzed for Tree-baseGraph({TG}_{n}) . {TG}_{n} graph has network cost O(6n) with a fixed degree of three and diameter 2n-2 . From the network cost viewpoint, {TG}_{n} has around 50% improvement results compared to existing fixed degree graphs such as mesh, torus, honeycomb mesh and shuffle-exchange permutation.