Graph Construction Algorithms Balances Randomness and Temporal Efficiency

Currently, graph data construction algorithms suffer from insufficient randomness, difficulty in constructing boundary data, and easy degradation of complexity when dealing with boundary data. In this paper, for the construction scenarios of non-repeating edge weights in graph data and cactus graphs, new algorithms that balance randomness and time efficiency are proposed, and the time and space complexities of these algorithms are optimized. In the experiments of edge weight construction, the spatiotemporal complexity of the new algorithms remains stable without being affected by extreme data while ensuring randomness. For dense random cactus graphs, a construction algorithm optimized based on the greedy idea is proposed. The experimental results show that, under different orders of magnitude of node numbers, the number of tree chains dissected by this algorithm is significantly higher than that of the unoptimized algorithm.