Efficient Haplotype Block Partitioning and Tag SNP Selection Algorithms under Various Constraints

Algorithm 1

The exhaustive searching algorithm for tag SNP selection.

FINDTAG(𝐵,𝜌)    ▷ Find the number of tag SNPs required for haplotype block 𝐵

        such that 𝜌 percentage of unambiguous haplotypes in 𝐵 can be

        distinguished uniquely.

Input: A percentage 𝜌 and haplotype block 𝐵 with unambiguous haplotype pattern

   𝑃={𝑝₁,𝑝₂,…,𝑝_𝑘}; the haplotypes number in each pattern is 𝑛₁,𝑛₂,…,𝑛_𝑘.

Output: The tag SNPs required for haplotype block 𝐵.

(1) Sort 𝑘 haplotype patterns in 𝑃=𝑝₁,𝑝₂,…,𝑝_𝑘.

   ▷  𝑝_𝑖’s are listed in decreasing order of the number of haplotype strings.

(2) 𝑈=𝜌⋅∑^𝑘_𝑖=1𝑛_𝑖    ▷  𝑈 is the number of 𝜌 percentage of unambiguous haplotypes.

(3) Find the minimum number 𝑔 such that ∑^𝑔_𝑖=1𝑛_𝑖≥𝑈

(4) 𝑡←log₂𝑔    ▷  𝑡 is the minimum number of tag SNPs required.

(5) for  𝑖←1  to  𝑡−1  do    ▷ initiate the tag SNP loci set {𝑎[1],𝑎[2],…,𝑎[𝑡]}.

(6)   𝑎[𝑖]←𝑖

(7) 𝑎[𝑡]←𝑎[𝑡−1];ℎ←0

(8) while  ℎ<𝑈  do    ▷  ℎ is the total haplotype strings that can be distinguished.

(9)   𝑖←𝑡    ▷  generate the next 𝑡-combination in lexicographic order.

(10)    while  𝑎[𝑖]=𝑙−𝑡+𝑖  do    ▷  𝑙 is the length of haplotype string.

(11)       𝑖←𝑖−1

(12)   if  𝑖=0

(13)    𝑡←𝑡+1

(14)     for  𝑖←1  to  𝑡  do

(15)     𝑎[𝑖]←𝑖

(16)   else

(17)    𝑎[𝑖]←𝑎[𝑖]+1

(18)     for  𝑗←𝑖+1  to  𝑡  do

(19)     𝑎[𝑗]←𝑎[𝑖]+𝑗−𝑖

(20)   ℎ←∑𝑛_𝑥, 𝑥∈{𝑥∣𝑝_𝑥 is the haplotype that can be distinguished by tag SNP.}

(21) return  𝑡