Algorithm 1: FDHE-IW

Inputs: D (s1, s2, …, sN, C)—the given data set with N + 1 columns; si denotes the values of the ith SNP locus for all samples. T—the candidate size; θ—the threshold of the G-test p-value; k—the number of SNPs in a k-way SNP combination; and K—the number to find the SNP combinations based on a seed SNP. Outputs: SNP combinations (SC)—the k-way SNP combinations that are associated with disease status.

(1)Initialize: $S^0=\left\{s_1,s_2,\dots ,s_N\right\},SC=\varnothing ,k=0,F=S^0$ (2)Calculate the $SU$ for each SNP.  For i = 1 to N do   Calculate $SU\left(s_i,C\right),s_i\in S^0$   $W\left(s_i\right)\leftarrow 1$  End For

(3)  Search a k-way SNP combination based on the interaction weight. (3.1) Select a SNP locus with a maximum$\mathit{S}\mathit{U}\times \mathit{W}$value.  $s_a\leftarrow \underset{s_i\in F}{{\displaystyle \mathbf{arg}\mathbf{max}}}SU(s_i,C)\times W(s_i),i=1,2,\dots ,N$ (3.2)  Search SNP combination based on interaction weight m = 1 While m < K || // to find K k-way SNP combinations based on $s_a$    $S\leftarrow \varnothing$    $\begin{array}{l}S\leftarrow S\cup \left\{s_a\right\}\\ F\leftarrow F\backslash \left\{s_a^{}\right\}\\ W(s_a)\leftarrow 0\end{array}$     While $\left|S\right|$ < k // $\left|S\right|$ is the SNPs number in S.      For i = 1 to |F| do // |F| denotes the SNPs number in F.         $IW\left(s_i\right)\leftarrow IWF\left(s_i,s_a;C\right),s_i\in F$ // Calculate interaction weight between si and Fa:         $W\left(s_i\right)\leftarrow W\left(s_i\right)\times IW\left(s_i\right),s_i\in F$ // Update the weight coefficient.         // calculate relevance between $s_i$ and phenotype (C)         $R\left(s_i,C\right)\leftarrow W\left(s_i\right)\times \left(1+SU(s_i,C\right)),I=1,2,\dots ,|S|$      End For $s_a\leftarrow \underset{s\in F}{{\displaystyle \arg \max R(s,C)}}$ // Select out the SNP $s_a$ that has maximum relevance with C in F.      $S\leftarrow S\cup \{s_a)$      $F\leftarrow F\backslash s_a$ // remove SNP $s_a$ from F.    End While    $SC\leftarrow SC\cup \left\{S\right\}$ // Store the found SNP combination S into SC as a candidate solution.    m = m + 1   End While (4) If the size of SC is less than T go to step (3) to find new k-way SNP combination that are associated with disease status. EndIf (5)  Statistical test Perform G-test statistic for each SNP combination in SC. Output the k-way SNP combinations with a p-value < θ