Symmetry in Algorithmic Graph Theory and Interconnection Networks

Dear Colleagues,

Graph theory is an ancient but very active mathematical discipline that deals with the study of graphs, which are mathematical structures used to model relationships between objects. A graph consists of a set of vertices (nodes) and edges (connections) that link these vertices. Graph theory provides a powerful framework for analyzing and solving problems involving networks, such as interconnection networks, social networks, complex networks, transportation systems, and computer networks. It offers a rich collection of algorithms and concepts for understanding connectivity, paths, cycles, and other fundamental properties of graphs.

Interconnection networks are crucial in the design of large-scale computer systems, such as parallel computers, distributed systems, and high-performance computing clusters. Interconnection networks are typically represented as graphs, with nodes representing processing processors and edges representing communication links. Graph theory plays a vital role in analyzing the properties and performance of interconnection networks.

Symmetry is a fundamental concept found in various scientific disciplines. Many interconnection networks have symmetrical structures and possess high symmetry due to their recursive construction and their vertex-transitive and edge-transitive properties, and thus are used in parallel systems. Symmetry plays a crucial role in understanding and exploiting the inherent regularity and structure of networks.

Algorithms are used to solve a wide range of problems, including graph traversal, shortest paths, network routing, and network optimization. Symmetry-based algorithms enable the identification of symmetrical patterns within networks, leading to enhanced system performance and communication efficiency, reduced latency and resource utilization, and efficient resource allocation, fault tolerance, and load balancing.

Contributions pursuing solutions to graph theory problems with algorithms as well as for interconnection networks are welcome.

Dr. Dongqin Cheng
Prof. Dr. Jou-Ming Chang
Dr. Chengkuan Lin
Guest Editors

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