This research article introduces bounded sparse dynamic programming (BSDP) as a method for rapidly approximating exhaustive sequence alignment. The approach is integrated into a framework that allows the automated development of efficient heuristic implementations for a wide range of sequence comparison problems. BSDP is used to generate alignments that are close to optimal but computed much faster than exhaustive methods. The system has been incorporated into the freely available sequence alignment program, exonerate. The paper discusses the use of finite state automata to describe alignment models and the transformation of these models into dynamic programming (DP) recurrence relations. This allows for the automated implementation of alignment algorithms. However, traditional DP methods require quadratic time, which is computationally expensive for large-scale applications. BSDP addresses this by applying DP only to small regions around alignment seeds, significantly reducing computation time. The paper also describes the automated generation of models for DP in SARs (sub-alignment regions). These models are derived from the original alignment model and are used to perform DP in specific regions of the alignment. The system uses priority queues to manage the alignment process, ensuring that the highest scoring paths are prioritized. Upper bounds are calculated for each SAR to determine whether DP is necessary, allowing for efficient alignment generation. The system is tested against other alignment methods, such as BLAST and EST_GENOME, and shows comparable accuracy with significantly faster performance. The approach is particularly effective for complex models, such as those used in GeneWise, and allows for the integration of features like introns into the alignment process. The paper concludes that BSDP provides a powerful framework for the automated generation of heuristics for sequence alignment, enabling the efficient handling of complex alignment models. The system is implemented in C and is available as part of the exonerate sequence alignment package. The framework is well-suited for a wide range of sequence comparison problems and has been applied to various biological datasets.This research article introduces bounded sparse dynamic programming (BSDP) as a method for rapidly approximating exhaustive sequence alignment. The approach is integrated into a framework that allows the automated development of efficient heuristic implementations for a wide range of sequence comparison problems. BSDP is used to generate alignments that are close to optimal but computed much faster than exhaustive methods. The system has been incorporated into the freely available sequence alignment program, exonerate. The paper discusses the use of finite state automata to describe alignment models and the transformation of these models into dynamic programming (DP) recurrence relations. This allows for the automated implementation of alignment algorithms. However, traditional DP methods require quadratic time, which is computationally expensive for large-scale applications. BSDP addresses this by applying DP only to small regions around alignment seeds, significantly reducing computation time. The paper also describes the automated generation of models for DP in SARs (sub-alignment regions). These models are derived from the original alignment model and are used to perform DP in specific regions of the alignment. The system uses priority queues to manage the alignment process, ensuring that the highest scoring paths are prioritized. Upper bounds are calculated for each SAR to determine whether DP is necessary, allowing for efficient alignment generation. The system is tested against other alignment methods, such as BLAST and EST_GENOME, and shows comparable accuracy with significantly faster performance. The approach is particularly effective for complex models, such as those used in GeneWise, and allows for the integration of features like introns into the alignment process. The paper concludes that BSDP provides a powerful framework for the automated generation of heuristics for sequence alignment, enabling the efficient handling of complex alignment models. The system is implemented in C and is available as part of the exonerate sequence alignment package. The framework is well-suited for a wide range of sequence comparison problems and has been applied to various biological datasets.