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Table 1 Time complexity of different applications

From: Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

Application output size standard CGR quadtree CGR Suffix Tree
LCE 1 O(1) O(1) O(1)
k-mismatch N O(kN) O(kN) O(kN)
Exact palindromes N O(N) O(N) O(N)
k-mismatch 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)
k-mismatch 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)
  1. This time complexity analysis does not include the pre-processing 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.