Lecture 4 - String Difference

Question 1

Applications of string distance?

Answer 1

• biology (DNA and protein sequences)
• file comparison (diff on Unix)
• spelling correction, speech recognition

Question 2

What is string distance?

Answer 2

What is the smallest number of basic operations needed to transform s to t?

Question 3

What are the 3 basic operations in transforming strings?

Answer 3

insert
delete
substitute

Question 4

Is it possible to have a model with costs allocated to operations?

Answer 4

Yes, our example in the lectures focuses on UNIT MODEL.

Question 5

What is the unit model for string distance?

Answer 5

Where each of the basic 3 operations costs 1 unit.

Question 6

What do string comparison algorithms use?

Answer 6

dynamic programming

Question 7

How is dynamic programming used in string transformations?

Answer 7

We build up a table of solutions to sub problems that get bigger and bigger. This is caleld the TABULAR METHOD. Eventually one of the values is the optimal answer.

Question 8

What is string distance?

Answer 8

Amount of operations one has to do to transfrom a string t to string s.

Question 9

What is string transformation?

Answer 9

Actual process of changing string t to string s.

Question 10

Our dynamic programming method for string transformation and distance is what …

Answer 10

edit distance

Question 11

What are the 4 cases for string transformations?

Answer 11

• match
• mismatch replace
• mistmatch delete
• mismatch insert

Question 12

In the tabular method what is insert?

Answer 12

left element i.e. d(i, j-1)

Question 13

In the tabular method what is delete

Answer 13

element on top i.e. d(i-1 , j)

Question 14

In the tabular method what is replace?

Answer 14

diagonal element i.e. d(i-1 , j-1)

Question 15

Why do we use the tabular method?

Answer 15

As it allows overlapping problems to be skipped, henceforth making the program more efficient

Question 16

What is the space complexity of string distance / transformation?

Answer 16

O(mn)

Question 17

How can we reduce the space complexity of the tabular method.

Answer 17

2 * string t length, as we only require the row above the current row, as well as the current row itself. This is O(n)

Question 18

What is the complexity of edit distance algorithm with the tabular method.

Answer 18

O(mn)

Question 19

What row / column can be filled in even before running the algorithm in the tabular method?

Answer 19

row 0 and column 0, simply replaced by the number of the square

d(i , 0) = i
d(0 , j) = j
* essentially index

Question 20

What is a vertical step in traceback?

Answer 20

substitution or match

Question 21

What is a horizontal step in traceback?

Answer 21

insert

Question 22

What is a vertical step in traceback?

Answer 22

delete

Question 23

Is traceback unique?

Answer 23

No, it can have many optimal alignments