1. String matching

2. Exact String Matching
Input: Two strings T[1…n] and P[1…m], containing symbols from alphabet .
Example:
 = {A,C,G,T}
T[1…12] = “CAGTACATCGAT”
P[1..3] = “AGT”
Goal: find all “shifts” 0≤s ≤n-m such that T[s+1…s+m] = P

3. Simple Algorithm for s ← 0 to n-m Match ← 1 for j ← 1 to m
if T[s+j]≠P[j] then
Match ← 0
exit loop
if Match=1 then output s

4. Analysis Running time of the simple algorithm: Worst-case: O(nm)
Average-case (random text): O(n) (expectation)
Ts = time spend on checking shift s
(the number of comparisons until 1st mismatch)
E[Ts] < 2 (why)
E[SsTs] = SsE[Ts] = O(n)

5. Approximate String Matching
Input: Two strings T[1…n] and P[1…m], containing symbols from alphabet .
Goal: find all “shifts” 0≤s ≤n-m such that T[s+1…s+m] is “highly similar” to P

6. Two common metrics for comparing strings
Given two strings T[1…n] and P[1…m]:
Hamming distance: the number of substitutions between the two strings. n=m
Edit distance: the number of edit operations (including substitutions, insertions, and deletions) to transform one string to the other string.

7. Simple Algorithm for Hamming Distance
for s ← 0 to n-m
Mismatch ← 0
for j ← 1 to m
if T[s+j]≠P[j] then
Mismatch ← Mismatch+1
If Mismatch > threshold exit loop
if Mismatch<=threshold then output s