Optimal tiling for the RNA base pairing problem

Abstract

Dynamic programming is an important combinatorial optimization technique that has been widely used in various fields such as control theory, operations research, computational biology and computer science. Many authors have described parallel dynamic programming algorithms for the family of multistage problems. More scarce is the literature for the more general class of problems where dependences appear between non-consecutive stages. Among the important problems falling in this class is the RNA base pairing problem. In this study we propose a new parallel scheme for a large class of recurrences with triangular iteration space and nonuniform dependences that includes the RNA base pairing problem. We derive two different instances of this scheme that correspond to an horizontal and a vertical traverse of the iteration domain. We develop and extend the tiling approach for this particular class. We formulate and analytically solve the optimization problem determining the tile size that minimizes the total execution time of the tiled program on a distributed memory parallel machine. Our analyze is based on the BSP model, which assures the portability of the obtained results. The computational experiments carried out on the CRAY T3E behave according to the predictions of our theoretical model.

A parallel dynamic programming algorithm on a multi-core architecture

“…For current machines it is an unrealistic approximation. Inspired by the blocking technique, F. Almeida [4] proposed a parallel implementation with tiling on a ring of processors. They showed the usefulness of the tiling technique for this nonuniform dependence DP.…”

Locality and Parallelism Optimization for Dynamic Programming Algorithm in Bioinformatics

“…The main difficulty for obtaining an efficient parallel implementation on distributed memory multicomputers system is to find a good balance between communication and computation costs. [J. H. Chen and Maizel 1998][F. Almeida and Gonzalez 2002] represent parallel implementations of RNA secondary structure prediction DP algorithm. In [J. H. Chen and Maizel 1998] the computational load balance is satisfactory but their designs do not optimize the communication cost.…”

“…The authors proved experimentally that the communications took about 50% of the execution time for a sequence with length of more than 9212. In [F. Almeida and Gonzalez 2002] the authors described blocked parallel implementation on a ring of processors and showed the usefulness of the tiling technique for this nonuniform dependences DP. They focused on reducing the communication costs.…”

“…But for current machines it is an unrealistic approximation. In [F. Almeida and Gonzalez 2002] the authors ignored that the computation of each iteration point was different, so their algorithm can not attain computation load balance. They overestimated the benefit of achieving the communication only between two neighbors and consequently kept the entire iteration space in each processor node.…”

“…In previous work [J. H. Chen and Maizel 1998][F. Almeida and Gonzalez 2002] for parallelizing the tile graph, the simple blockcyclic distribution maps tiles to the processors in a column/row wise modulo p fashion; i.e. row i is allocated to i mod p processor.…”