Fig. 2
From: An average-case sublinear forward algorithm for the haploid Li and Stephens model
Work done to calculate the sum of haplotype probabilities at a site for the conventional and our sublinear forward algorithm. Using the example that at site i, \(\phi _i(o_i) = \{h_3\}\), we illustrate the number of arithmetic operations used in (i) the conventional \(\mathcal {O}(nk)\) Li and Stephens HMM recurrence relations. ii Our procedure specified in Eq. (12). Black lines correspond to arithmetic operations; operations which cannot be parallelized over j are colored yellow