By C. Trullemans

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3 Wu-Manber algorithm The poor performance of the extension of Horspool to search a set of patterns is a direct consequence of the fact that the lengths of the shifts are usually decreasing, due to the high probability of finding each character of the alphabet in one of the strings. The algorithm of Wu and Manber [WM94] bypasses this obstacle by reading blocks of characters, which reduces the probability that each block appears in one of the patterns. We consider blocks of length B. The difficulty is that there could be ∣Σ∣B different blocks, requiring too much memory if B becomes large.

We shift the search position by 1. 5. AGATACGATA TAC SHIFT[TA] = 0. L = HASH[TA] = {1}. We compare p1 against the text. The test fails. We shift the search position by 1. 6. AGATACGATAT AC SHIFT[AT] = 0. L = HASH[AT] = {2, 3}. We compare p2 and p3 against the text. The string p2 matches. We mark its occurrence. We shift the search position by 1. Chapter 3: Multiple String Matching 47 48 Chapter 3: Multiple String Matching 7. AGATACGATATA C SHIFT[TA] = 0. L = HASH[TA] = {1}. We compare p1 against the text.

AGATACGATA We read C, A in the factor oracle and fail on the next T. We shift the window and the search stops since pos ≥ n – ℓmin. 5 Experimental maps We present in this section some maps of efficiency for the different multiple string matching algorithms, showing for all of them the zone in which they are most efficient in practice. The text of 10 megabytes is randomly built, as are the patterns. 6. The sets contain 5, 10, 100, and 1000 strings of the same length, varying from 5 to 100 in steps of 5.