The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization. However, such algorithms assume that generating point positions are given as inputs, while we usually do not know the positions in advance. In this study, we propose a method to automatically calculate the suitable point positions. The method uses (1) semidefinite programming to approximate locations while maintaining relative positions among locations; and (2) gradient descent to iteratively update locations subject to area constraints. We apply the proposed framework to a practical case at Chiang Mai University and compare its performance with a benchmark, the differential genetic algorithm. The results show that the proposed method is 28 times faster than the differential genetic algorithm, while the resulting land allocation error is slightly larger than that of the benchmark but still acceptable. Additionally, the output does not contain disconnected areas, as found in all evolutionary computations, and the compactness is almost equal to the maximum possible value.

Northern Thailand frequently suffers from severe PM2.5 air pollution, especially during the dry season, due to agricultural burning, local emissions, and transboundary haze. Understanding how pollution moves across regions and identifying source–receptor relationships are critical for effective air quality management. This study investigated the spatial and temporal dynamics of PM2.5 in northern Thailand. Specifically, it explored how pollution at one monitoring station influenced concentrations at others and revealed the seasonal structure of PM2.5 transmission using network-based analysis. We developed a Python-based framework to analyze daily PM2.5 data from 2022 to 2023, selecting nine representative stations across eight provinces based on spatial clustering and shape-based criteria. Delaunay triangulation was used to define spatial connections among stations, capturing the region’s irregular geography. Cross-correlation and Granger causality were applied to identify time-lagged relationships between stations for each season. Trophic coherence analysis was used to evaluate the hierarchical structure and seasonal stability of the resulting networks. The analysis revealed seasonal patterns of PM2.5 transmission, with certain stations, particularly in Chiang Mai and Lampang, consistently acting as source nodes. Provinces such as Phayao and Phrae were frequently identified as receptors, especially during the winter and rainy seasons. Trophic coherence varied by season, with the winter network showing the highest coherence, indicating a more hierarchical but less stable structure. The rainy season exhibited the lowest coherence, reflecting greater structural stability. PM2.5 spreads through structured, seasonal pathways in northern Thailand. Network patterns vary significantly across seasons, highlighting the need for adaptive air quality strategies. This framework can help identify influential monitoring stations for early warning and support more targeted, season-specific air quality management strategies in northern Thailand.

Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, at most, four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.

Keywords: Spatiotemporal Data Services and Knowledge Services, Land-Use Optimization Problem, Laguerre Voronoi Diagram, Force-Directed Graph Drawing, Linear Programming, Interactive Design In this work, we devise an efficient method for the land-use optimization problem based on Laguerre Voronoi diagram. Previous Voronoi diagram-based methods are more efficient and more suitable for interactive design than discrete optimization-based method, but, in many cases, their outputs do not satisfy area constraints. To cope with the problem, we propose a force-directed graph drawing algorithm, which automatically allocates generating points of Voronoi diagram to appropriate positions. Then, we construct a Laguerre Voronoi diagram based on these generating points, use linear programs to adjust each cell, and reconstruct the diagram based on the adjustment. We adopt the proposed method to the practical case study of Chiang Mai University’s allocated land for a mixed-use complex. For this case study, compared to other Voronoi diagram-based method, we decrease the land allocation error by 62.557 %. Although our computation time is larger than the previous Voronoi-diagram-based method, it is still suitable for interactive design.