Finding Common RNA Secondary Structures: A Case Study on the Dynamic Parallelization of a Data-driven Recurrence

This paper presents the dynamic parallelization of a sequential algorithm for finding common RNA secondary structures that initially does not appear to be amenable to parallelization. A critical insight into the problem structure, which at first appears to be inherently top-down, leads to the development of a revised sequential algorithm that uses both bottom-up tabulation and top-down memoization. This novel combined approach proves well-suited for parallelization, overcoming the inherent difficulties in parallelizing the original top-down algorithm. The improved algorithm also eliminates two factors from the space complexity to fit into quadratic space, enabling the comparison of lengthy and complex RNA structures. Experimental results demonstrate that the parallel algorithm scales well, achieving speedup of up to 32X using 64 processors for contrived worst-case data containing structures having up to 1600 nested arcs. This algorithm illustrates the significant benefits that can be achieved by designing an underlying sequential dynamic programming algorithm with parallelizability in mind, instead of directly parallelizing an existing sequential algorithm. Our results also show the usefulness of combining both bottom-up and top-down perspectives when designing a parallel dynamic programming algorithm.