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Restriction maps

The Double Digest Problem (DDP)

Task 1

  • In R, create a function DoubleDigestProblem() for the brute-force DDP algorithm for one possible arrangement of fragments.

  • Input:

    • a multiset of fragments generated by digestion by enzyme A
    • a multiset of fragments generated by digestion by enzyme B
    • a multiset of fragments generated by digestion by enzymes A + B

  • Output:

    • positions of restriction sites for enzyme A
    • positions of restriction sites for enzyme B

  • Modify it to search through all possible arrangements of fragments.

The Partial Digest Problem (PDP)

Task 2

  • In R, implement a function Place() according to the following pseudocode.

  • Input:

    • a multiset of fragments lengths
    • a list of the current positions of the restriction sites
    • length of the DNA molecule i.e. the size of the longest fragment

  • Output:

    • a list of the positions of the restriction sites

  • Δ(y, X) is a multiset of lengths between value y and all values in X.

  • Hint: Create additional function Remove(), which removes from deltaX all used lengths Δ(y, X).

Place(deltaX, X, width)
1   if deltaX is empty
2     output X
3     return
4   y ← the maximum element from deltaX
5   if Δ(y, X) ⊆ deltaX
6     add y to X and remove the lengths Δ(y, X) from deltaX
7     Place(deltaX, X, width)
8     remove y from X and add the lengths Δ(y, X) to deltaX
9   if Δ(width - y, X) ⊆ deltaX
10    add width - y to X and remove the lengths Δ(width - y, X) from deltaX
11    Place(deltaX, X, width)
12    remove width - y from X and add the lengths Δ(width - y, X) to deltaX
13  return

Task 3

  • In R, implement a function PartialDigestProblem() according to the following pseudocode.

  • Input:

    • a multiset of fragments lengths
PartialDigestProblem(deltaX)
1   width ← the maximum element from deltaX
2   delete the maximum element from deltaX
3   X ← {0, width}
4   Place(deltaX, X, width)
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