On the computational complexity of Dempster’s Rule of combination, a parallel computing approach

Abstract

Multisensor data fusion with Dempster–Shafer (D–S) theory is beneficial for context inference without any advanced information. D–S theory includes reasoning based on Dempster’s rule of combination of degrees of belief based on different pieces of evidence. Although, the computational complexity of Dempster’s rule of combination is enormous. Any change in the number of pieces of evidence or hypotheses causes a lot of additional computations. Dempster’s rule of combination is shown to be #P-complete. The combination rule of k frames of evidence with nk elements, such that (k∈N|k≥2) has a time complexity of O(2N), where N=∑knk. In this paper, we propose a parallel computing approach for Dempster’s rule of combination based on the concept of conquer and divide algorithms. The proportion of task benefiting from improvement is p=1−2k, hence k2 of theoretical maximum speed-up according to Amdahl’s law. We have tested our algorithm in different experimental settings and observed that the new parallel computing approach has not only achieved the best results in CPU version, but has also outperformed GPU version using Thrust CUDA in almost scenarios of the experiment.