Genetic-Score-Mapping
Scenario
You are a Genetics researcher working on phylogeny data – you have gene sequences of various organisms. You want to prove that some organisms are more related than others. You decide to map the strings onto each other and calculate mapping scores between each pair of organisms. The organisms with lower map scores probably are more related. Similarly, later you may have multiple organisms and you want to prove that they are all cumulatively related. The computational task is to compute an overall mapping score for a group of strings
Problem Statement
There are K strings Xi from the vocabulary V. Each string Xi has length Ni. Your goal is to map the strings to each other. An easy way to do this is to think of this in two steps – conversion and matching. Conversion is a function F that takes in a string and returns another string. All F(Xi)s have the same length N. N is greater than equal to all Nis. The function F is only allowed to make one change to the original string – it can introduce dashes. It can introduce any number of dashes at any position. The conversion cost of X to F(X) is CC * number of dashes, CC being a constant. Once all strings have been converted the matching step just matches characters at each position. The matching cost between two characters is given by a symmetric function MC(c1, c2) where c1 and c2 are two characters ϵ V U {-}. Matching cost of two strings is the sum of matching costs of their conversions at each position. Finally, the matching cost of K strings is the sum of pairwise matching costs between each pair
Input Format
Time (in mins)
|V|
V
K
X1
X2
…
CC
MC
#
Here is the format of MC is that it is representing a matrix of |V|+1 rows and columns. The last row and column is for dash. All diagonal entries will be zero. Any other entry represents the MC between the appropriate characters in V (based on the order they appear in V in the input line number 3). # represents end of the file
Output Format
F(x1)
F(x2)
...
Example
Let K =3. Let vocabulary V= {A,C,T,G}. Suppose the three strings Xis are:
X1: ACTGTGA
X2: TACTGC
X3: ACTGA
So, for this problem N1, N2, N3 are 7, 6 and 5 respectively. Let all costs be as follows: CC = 3, MC(x,y) = 2 if x, y ϵ V and x != y; MC(x, -) = 1; MC(x, x) = 0. We may define our conversions as follows:
F(X1): -ACTGTGA
F(X2): TACT--GC
F(X3): -ACTG--A
With these conversions N = 8. The conversion costs are respectively 3, 6, and 9. The matching cost between F(X1) and F(X2) is 1+0+0+0+1+1+0+2 = 5. Similarly between F(X2) and F(X3) is 1+0+0+0+1+0+1+2=5 and between F(X1) and F(X3) is 0+0+0+0+0+1+1+0=2. Hence the total matching cost of this conversion is 5+5+2=12
The final output cost of this mapping problem is sum of conversion and matching costs = 3+6+9+12=30.
The goal is to find a conversion with the lowest final cost. (The current solution is not the optimal solution for this problem)
Input format here
5.5
4
A, C, T, G
3
ACTGTGA
TACTGC
ACTGA
3
0 2 2 2 1
2 0 2 2 1
2 2 0 2 1
2 2 2 0 1
1 1 1 1 0
#
Output Format here
ACTGTGA
TACT--GC
-ACTG—A
Implementation
A state space and transition function were defined and a heuristic search was developed for this. Also, a local search was implemented with the Neighbours being defined as the ones which differ by the position of one Dash (-). The program can be run by compiling the file by doing ./compile.sh and then ./run.sh input.txt output.txt