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We focus on Text-to-SQL semantic parsing from the perspective of retrieval-augmented generation. Motivated by challenges related to the size of commercial database schemata and the deployability of business intelligence solutions, we propose $\text{ASTReS}$ that dynamically retrieves input database information and uses abstract syntax trees to select few-shot examples for in-context learning. Furthermore, we investigate the extent to which an in-parallel semantic parser can be leveraged for generating approximated versions of the expected SQL queries, to support our retrieval. We take this approach to the extreme--we adapt a model consisting of less than $500$M parameters, to act as an extremely efficient approximator, enhancing it with the ability to process schemata in a parallelised manner. We apply $\text{ASTReS}$ to monolingual and cross-lingual benchmarks for semantic parsing, showing improvements over state-of-the-art baselines. Comprehensive experiments highlight the contribution of modules involved in this retrieval-augmented generation setting, revealing interesting directions for future work., Comment: EMNLP 2024 Main