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

• Published in: IEEE access Vol. 11; pp. 120816 - 120826
• Main Authors: Seong, Bo Ok, Jang, Jin-Hyeok, Lee, Hyeong Ok
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Binary trees; Cost analysis; Costs; Diameters; Fixed degree; full binary tree; Hypercubes; Indexes; Interconnected systems; interconnection network; network cost; parallel paths; Parallel processing; Permutations; Program processors; Toruses
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2023.3326853

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 <inline-formula> <tex-math notation="LaTeX">\ast </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">Tree-baseGraph({TG}_{n}) </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">Tree-baseGraph({TG}_{n}) </tex-math></inline-formula>. <inline-formula> <tex-math notation="LaTeX">{TG}_{n} </tex-math></inline-formula> graph has network cost <inline-formula> <tex-math notation="LaTeX">O(6n) </tex-math></inline-formula> with a fixed degree of three and diameter <inline-formula> <tex-math notation="LaTeX">2n-2 </tex-math></inline-formula>. From the network cost viewpoint, <inline-formula> <tex-math notation="LaTeX">{TG}_{n} </tex-math></inline-formula> has around 50% improvement results compared to existing fixed degree graphs such as mesh, torus, honeycomb mesh and shuffle-exchange permutation.