For scalable autonomous driving, a robust map-based localization system, independent of GPS, is fundamental. To achieve such map-based localization, online high-definition (HD) map construction plays a significant role in accurate estimation of the pose. Although recent advancements in online HD map construction have predominantly investigated on vectorized representation due to its effectiveness, they suffer from computational cost and fixed parametric model, which limit scalability. To alleviate these limitations, we propose a novel HD map learning framework that leverages graph modeling. This framework is designed to learn the construction of diverse geometric shapes, thereby enhancing the scalability of HD map construction. Our approach involves representing the map elements as an instance-level graph by decomposing them into vertices and edges to facilitate accurate and efficient end-to-end vectorized HD map learning. Furthermore, we introduce an association strategy using a Graph Neural Network to efficiently handle the complex geometry of various map elements, while maintaining scalability. Comprehensive experiments on public open dataset show that our proposed network outperforms state-of-the-art model by $1.6$ mAP. We further showcase the superior scalability of our approach compared to state-of-the-art methods, achieving a $4.8$ mAP improvement in long range configuration. Our code is available at https://github.com/juyebshin/InstaGraM.

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