Table 6.

gammaMAXT parallel workflow

(1) Each cluster node $c=1\dots C$ performs an equitable fraction of the computations of the T 0,1,…,T 0,m

values from Fig. 1. The n highest values (and corresponding SNP pair indexes) from each node are saved

into file top_c.txt.

(2) Upon termination of all computations at the previous step, a cluster node aggregates all top_c.txt files and

retrieves the overall n highest values (and corresponding SNP pair indexes). Results are saved into topfile.txt.

(3) Each cluster node reads topfile.txt, initialize a vector V of size n with 0’s and performs an equitable fraction

of the B permutations of Fig. 1. For each permutation i attributed to node c:

(a) Generate a random permutation of the trait column.

(b) Compute T i,1,…,T i,n and store them in a Permutation i vector.

(c) Execute step (3)(c) of the gammaMAXT algorithm to estimate M i.

(d) Replace T i,n by M i if T i,n<M i.

(e) Force the monotonicity of the Permutation i vector: for j=n−1,…,1 replace T i,j by T i,j+1 if T i,j<T i,j+1.

(f) For each j=1,…,n, if T i,j≥T 0,j increment V j by one.

Upon completion of all computations on node c, save V into file permut_c.txt.

(4) A cluster node sums all vectors from the permut_c.txt files to obtain a vector p. All elements of p are

incremented by 1 and divided by B+1. The monotonicity is forced: for j=1,…,n−1, replace p j+1 by p j

if p j+1<p j.