Speeding-up hirschberg and hunt-szymanski LCS algorithms

Speeding up transposition-invariant string matching

“…• BBB-a binary branch and bound method [8] of complexity O((mn + log σ )σ ) in the worst case and O((mn + log log σ ) log σ ) in the best case, • CDP-a classical dynamic programming repeated for all t ∈ [−σ, σ ] of complexity O(mnσ ) [10], • KBB-a k-ary branch and bound method [8] of complexity O((mn + log(σ k/(k − 1)))σ k/(k − 1)) in the worst case and O((mn + log(k log k σ ))k × log k σ ) in the best case (we used k = 3 in our experiments, following [8] where the authors found that this value is the best in their experiments; the choice of k was also confirmed in our preliminary experiments), • SDP-a sparse dynamic programming [11] of complexity O(mn log m), • YBP-a bit-parallel algorithm [2] of complexity O(mn σ/w ), where w is the machine word size (in bits), • HBP-a bit-parallel LCS algorithm [6] repeated for all possible t values of complexity O( n/w mσ ), • NGMD-a recent algorithm [14] of complexity O(mn log log σ ).…”

Incremental Multiple Longest Common Sub-Sequences

“…In particular both the points we mentioned are part of the MLCS in the top box of Figure 1. On the contrary the match (2,9,4,8), corresponding to letter 'B', does not dominate the match (4, 2, 1, 1), because in the first coordinate we have 2 < 4. These two matches are not compatible and therefore may not both occur in a MCS.…”

“…1 (1,9,4,8); (4,2,1,1) ; (15,1,2,2) 2 (2,11,8,9); (4,10,5,10); (5,9,4,8); (6,3,5,3) ; (15,4,2,2); (16,2,5,3) 3 (3,12,9,14); (4,13,10,10); (5,11,8,14); (6,10,5,10); (7,5,7,4) ; (15,4,6,…”

Towards Efficient Analysis for Malware in the Wild

“…Since the amount of malware is increasing, we need a faster algorithm for finding an LCS. Crochemore et al [10] have proposed a bit-vector algorithm with a processing time of O( MN w ), where w is the number of bits in a machine word. The method assigns one bit to a cell in the DP matrix, and calculates w cells in bulk using four operations (and, or, not and add).…”