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We present a design methodology that enables the semi-automatic generation ofa hardware-accelerated graph building architectures for locally constrainedgraphs based on formally described detector definitions. In addition, we definea similarity measure in order to compare our locally constrained graph buildingapproaches with commonly used k-nearest neighbour building approaches. Todemonstrate the feasibility of our solution for particle physics applications,we implemented a real-time graph building approach in a case study for theBelle~II central drift chamber using Field-Programmable Gate Arrays~(FPGAs).Our presented solution adheres to all throughput and latency constraintscurrently present in the hardware-based trigger of the Belle~II experiment. Weachieve constant time complexity at the expense of linear space complexity andthus prove that our automated methodology generates online graph buildingdesigns suitable for a wide range of particle physics applications. By enablingan hardware-accelerated pre-processing of graphs, we enable the deployment ofnovel Graph Neural Networks~(GNNs) in first level triggers of particle physicsexperiments.

Real-time Graph Building on FPGAs for Machine Learning Trigger Applications in Particle Physics