Application

output size

standard CGR

quadtree CGR

Suffix Tree


LCE

1

O(1)

O(1)

O(1)

kmismatch

N

O(kN)

O(kN)

O(kN)

Exact palindromes

N

O(N)

O(N)

O(N)

kmismatch palindromes

N

O(kN)

O(kN)

O(kN)

Exact tandem repeats

z

O(N log N + z)

O(N log N + z)

O(N log N + z)

kmismatch tandem repeats

z

O(kN log N + z)

O(kN log N + z)

O(kN log N + z)

Longest common suffix

1

O(1)

O(1)

O(1)

Exact match (MATCHES)

occ

O(N)

O(L + occ)

O(L + occ)

Occurrences (COUNT)

1

O(N)

O(L + occ)

O(L + occ)

Longest common substring

1

O(N log N)

O(N log N)

O(N)

 This time complexity analysis does not include the preprocessing step of building the required indexes, as all depend solely in the size N of the input string S. In the following L is the length of pattern P.