. 2009 Mar 4;7:75–89. doi: 10.4137/cin.s1054

Table 4.

Average case complexity for the proposed algorithms.

Complexity		Alg. 1	Alg. 2	Alg. 3
Time	Construction	O(n_sl_s) O(\|S_d\|)	O(n_sl_s + n_pl_p)	O(n_pl_p) = O(\|S_c\|)
	Search	O(n_sn_pl_p) O(n_s\|S_c\|)	O(n_pl_p)	O(n_sl_s) = O(\|S_d\|)
	Total	O(n_sl_s + n_sn_pl_p) ≈ O(n_sl_s)	O(n_sl_s + n_pl_p) ≈O(n_sl_s)	O(n_sl_s + n_pl_p) ≈O(n_sl_s)
Space	Construction	O(w_s)	O(n_sl_s + n_pl_p)	O(n_pl_p)
	Search	O(l_p)	O(l_p)	O(w_s)
	Total	O(w_s + l_p) ≈ O(w_s)	O(n_sl_s + n_pl_p) ≈ O(n_sl_s)	O(n_pl_p) + O(w_s).≈ O(w_s)

Average case complexity for the proposed algorithms (n_s = number of sequences in the database, n_p = number of common patterns, i_s = average length of a sequence, i_p = average length of a pattern, w_s = number of characters processed at one time (size of the sliding window), s_c is the concatenation of all the multiple patterns, and s_d is the concatenation of all the sequences in the database).