Algorithm 4

Profile alignment with FM-index

Input: nucleotide profiles |${P}_1\ \mathrm{and}\ {P}_2$|
Output: aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Assume |$len\left({P}_1\right)\ge len\left({P}_2\right)$|
1. Simplify |${P}_1\ \mathrm{and}\ {P}_2$| as two modified consensus sequences |${S}_1\ \mathrm{and}\ {S}_2$|⁠.
2. Build the FM-index for |${S}_1$|⁠.
3. While |$i< len\left({S}_2\right)$|⁠, |$i$| starts at 1.
Begin index |$i$| in |${S}_2$| to find the longest common substrings |$lc{s}_j$| in |${S}_1$|⁠.
i + = len(lcsj)
4. The selection of optimized longest and non-overlapped common substring combinations.
5. Directly align the profile region relative to the optimized common substrings, and use k-banded DP to align the remaining profile segments individually. Join all aligned segments together to return the aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Input: nucleotide profiles |${P}_1\ \mathrm{and}\ {P}_2$|
Output: aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Assume |$len\left({P}_1\right)\ge len\left({P}_2\right)$|
1. Simplify |${P}_1\ \mathrm{and}\ {P}_2$| as two modified consensus sequences |${S}_1\ \mathrm{and}\ {S}_2$|⁠.
2. Build the FM-index for |${S}_1$|⁠.
3. While |$i< len\left({S}_2\right)$|⁠, |$i$| starts at 1.
Begin index |$i$| in |${S}_2$| to find the longest common substrings |$lc{s}_j$| in |${S}_1$|⁠.
i + = len(lcsj)
4. The selection of optimized longest and non-overlapped common substring combinations.
5. Directly align the profile region relative to the optimized common substrings, and use k-banded DP to align the remaining profile segments individually. Join all aligned segments together to return the aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Algorithm 4

Profile alignment with FM-index

Input: nucleotide profiles |${P}_1\ \mathrm{and}\ {P}_2$|
Output: aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Assume |$len\left({P}_1\right)\ge len\left({P}_2\right)$|
1. Simplify |${P}_1\ \mathrm{and}\ {P}_2$| as two modified consensus sequences |${S}_1\ \mathrm{and}\ {S}_2$|⁠.
2. Build the FM-index for |${S}_1$|⁠.
3. While |$i< len\left({S}_2\right)$|⁠, |$i$| starts at 1.
Begin index |$i$| in |${S}_2$| to find the longest common substrings |$lc{s}_j$| in |${S}_1$|⁠.
i + = len(lcsj)
4. The selection of optimized longest and non-overlapped common substring combinations.
5. Directly align the profile region relative to the optimized common substrings, and use k-banded DP to align the remaining profile segments individually. Join all aligned segments together to return the aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Input: nucleotide profiles |${P}_1\ \mathrm{and}\ {P}_2$|
Output: aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
Assume |$len\left({P}_1\right)\ge len\left({P}_2\right)$|
1. Simplify |${P}_1\ \mathrm{and}\ {P}_2$| as two modified consensus sequences |${S}_1\ \mathrm{and}\ {S}_2$|⁠.
2. Build the FM-index for |${S}_1$|⁠.
3. While |$i< len\left({S}_2\right)$|⁠, |$i$| starts at 1.
Begin index |$i$| in |${S}_2$| to find the longest common substrings |$lc{s}_j$| in |${S}_1$|⁠.
i + = len(lcsj)
4. The selection of optimized longest and non-overlapped common substring combinations.
5. Directly align the profile region relative to the optimized common substrings, and use k-banded DP to align the remaining profile segments individually. Join all aligned segments together to return the aligned profiles |${P}_{a1}\ \mathrm{and}\ {P}_{a2}$|
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