The article introduces a novel approach called Bounded Sparse Dynamic Programming (BSDP) for rapid approximation of exhaustive sequence alignment. BSDP is designed to balance speed and accuracy, making it suitable for large-scale genome analysis. The method is automated, allowing for the development of efficient heuristic implementations of complex alignment models. The authors describe the framework that connects the underlying alignment models to the heuristics, enabling the automated generation of efficient code. BSDP is demonstrated through examples in genome annotation and compared favorably with existing methods in terms of speed and accuracy. The system has been integrated into the sequence alignment program Exonerate, which is freely available. The article also discusses the limitations of the approach, particularly in handling distantly related sequences with many gaps. Overall, BSDP represents an advancement in the automatic implementation of sequence alignment algorithms, making complex heuristics more practical for a broader range of problems.The article introduces a novel approach called Bounded Sparse Dynamic Programming (BSDP) for rapid approximation of exhaustive sequence alignment. BSDP is designed to balance speed and accuracy, making it suitable for large-scale genome analysis. The method is automated, allowing for the development of efficient heuristic implementations of complex alignment models. The authors describe the framework that connects the underlying alignment models to the heuristics, enabling the automated generation of efficient code. BSDP is demonstrated through examples in genome annotation and compared favorably with existing methods in terms of speed and accuracy. The system has been integrated into the sequence alignment program Exonerate, which is freely available. The article also discusses the limitations of the approach, particularly in handling distantly related sequences with many gaps. Overall, BSDP represents an advancement in the automatic implementation of sequence alignment algorithms, making complex heuristics more practical for a broader range of problems.