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.