Generation of Multi-Level Regular Networks Based on the Composition Operation of Modified Chordal Graphs Using Large Language Models

The paper is devoted to the development and study of a new class of topologies for communication networks used in multiprocessor systems and networks-on-chip. The primary goal of this paper is to solve the problem of network topology optimization. Key network characteristics are its diameter (the maximum shortest distance between any two nodes) and the average distance between nodes: the smaller these parameters, the lower the data transmission latency and the higher the overall system performance. The goal of this paper is to propose a new network construction model that achieves better performance (smaller average distance) compared to existing optimal circulant networks with the same hardware costs (i. e., the same number of nodes and links). The paper proposes a new method for constructing multi-level networks and introduces a new operation, multi-level composition, which allows the use of a wide range of regular graphs, previously proposed as computing system structures, as layer elements, combining them optimally. In this paper, the operation of multi-level composition is applied to a class of chordal rings and modified chordal graphs. The essence of the method is as follows: 1. Level creation: The network is constructed from several (m) levels. Each level is a regular graph (in this paper, a chordal graph g1). In the first step, m disconnected copies of this graph are created. 2. Level connection: All nodes from all levels are connected to each other via a second, “global” graph (G2), which is also chordal. The result is a new, more complex regular network G, which is the sum of the graphs G1 (intra-level connections) and G2 (inter-level connections). To find the best configuration of such a network (i. e., to find the generators for graphs g1 and G2), the authors use the Simulated Annealing algorithm. This algorithm allows for efficient finding of parameters that minimize the average distance in the resulting network. The algorithm for synthesizing optimal multi-level networks was developed using large language models and implemented in sequential and parallel versions on the Kunpeng cluster. The authors conducted numerical simulations and compared their multi-layer networks with the best known circulant networks (C). Optimal (suboptimal) multi-layer regular networks of degrees 4 and 6 were obtained. The influence of multi-layer network parameters on the average distance including the number of levels was studied. The paper presents the key experimental results. (1) Improvement: in some configurations, for degree 4, the improvement reached more than 3 times compared to optimal circulant networks. (2) Scalability: the advantage of the new approach becomes more pronounced with an increasing number of nodes in the network. This makes it promising for building large computing systems and networks. (3) Use of AI in development: an interesting feature of the work is that the authors used large language models (LLM), such as Gemini-2.5Pro, to assist in writing and parallelizing C code for running simulations. According to the authors’ estimates, this reduced development time by 20–30 %. The article demonstrates the effectiveness of the new approach and convincingly demonstrates that the proposed multi-level composition operation is a new tool for constructing high-performance network topologies. The practical significance of the article lies in the fact that the resulting networks can be used to design real multiprocessor systems and networks-on-chip, providing lower latency and improved performance. The proposed method is general and can be applied in the future to other classes of graphs, not just chordal ones, opening up new avenues for research. The paper utilizes modern artificial intelligence tools and demonstrates the successful integration of modern AI assistants into scientific research and the development of complex software. Future work is planned to explore the use of other classes of graphs to obtain multi-level regular networks, as well as to theoretically study their characteristics and the possibility of constructing efficient routing algorithms in such networks.