A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.In this paper,it is shown that 1-planar graphs with girth at least7 are（1,1,1,0）-colorable.
In edge-distributed environments,spatiotemporal graphs provide a promising solution for capturing the complex dependencies among nodes and edges necessary for accurate wind speed forecasting.These dependencies involve...In edge-distributed environments,spatiotemporal graphs provide a promising solution for capturing the complex dependencies among nodes and edges necessary for accurate wind speed forecasting.These dependencies involve spatial and temporal interactions that are crucial for modeling dynamic weather patterns.However,challenges,such as effectively maintaining spatial dependency information across spatiotemporal subgraphs,can lead to reduced prediction accuracy.Additionally,managing high communication costs,associated with the need for frequent and intensive data exchanges required for real-time forecasting across distributed nodes,poses significant hurdles.To address these issues,we propose graph coarsening-based cross-subgraph message passing with edge collaboration training mechanism(namely ComPact),a novel approach that simplifies graph structures through graph coarsening while preserving essential spatiotemporal dependencies.This coarsening process minimizes communication overhead and enables effective cross-subgraph message passing,capturing both local and long-range dependencies.ComPact further leverages hierarchical graph learning and structured edge collaboration to integrate global information into local subgraphs,enhancing predictive performance.Experimental validation on large-scale datasets,primarily the WindPower dataset,demonstrates ComPact’s superiority in wind speed forecasting,with up to a 31.82%reduction in Mean Absolute Error(MAE)and 11.8%lower in Mean Absolute Percentage Error(MAPE)compared to federated learning baselines.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11271365)the Joint Funds of Department of Education under the Natural Science Funds of Shandong Province(Grant No.ZR2014JL001)
文摘A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.In this paper,it is shown that 1-planar graphs with girth at least7 are（1,1,1,0）-colorable.
基金supported by the Science and Technology Project of State Grid Jiangsu Electric Power Co.Ltd.(No.J2023153).
文摘In edge-distributed environments,spatiotemporal graphs provide a promising solution for capturing the complex dependencies among nodes and edges necessary for accurate wind speed forecasting.These dependencies involve spatial and temporal interactions that are crucial for modeling dynamic weather patterns.However,challenges,such as effectively maintaining spatial dependency information across spatiotemporal subgraphs,can lead to reduced prediction accuracy.Additionally,managing high communication costs,associated with the need for frequent and intensive data exchanges required for real-time forecasting across distributed nodes,poses significant hurdles.To address these issues,we propose graph coarsening-based cross-subgraph message passing with edge collaboration training mechanism(namely ComPact),a novel approach that simplifies graph structures through graph coarsening while preserving essential spatiotemporal dependencies.This coarsening process minimizes communication overhead and enables effective cross-subgraph message passing,capturing both local and long-range dependencies.ComPact further leverages hierarchical graph learning and structured edge collaboration to integrate global information into local subgraphs,enhancing predictive performance.Experimental validation on large-scale datasets,primarily the WindPower dataset,demonstrates ComPact’s superiority in wind speed forecasting,with up to a 31.82%reduction in Mean Absolute Error(MAE)and 11.8%lower in Mean Absolute Percentage Error(MAPE)compared to federated learning baselines.
