knuth-morris-pratt

I tried to solve the problem of two dimensional search using a combination of Aho-Corasick and a single dimensional KMP, however, I still need something faster. To elaborate, I have a matrix A of characters of size n1*n2 and I wish to find all occurrences of a smaller matrix B of size m1*m2 and I want that to be in O(n1*n2+m1*m2) if possible. For example: A = a b c b c b b c a c a c d a b a b a q a s d q a and B = b c b c a c a b a the algorithm should return the indexes of say, the upper left corner of the match, which in this case should return (0,1) and (0,3). notice that the occurrences

I have generated an string using the following alphabet. {A,C,G,T} . And my string contains more than 10000 characters. I'm searching the following patterns in it. ATGGA TGGAC CCGT I have asked to use a string matching algorithm which has O(m+n) running time. m = pattern length n = text length Both KMP and Rabin-Karp algorithms have this running time. What is the most suitable algorithm (between Rabin-Carp and KMP) in this situation? Ivaylo Strandjev When you want to search for multiple patterns, typically the correct choice is to use Aho-Corasick , which is somewhat a generalization of KMP .

What is the theoretical basis of KMP pattern-matching algorithm? I understand the algorithm itself, but, don't understand how did Knuth, Morris and Pratt invent this algorithm. Was there any mathematical proof? Can you give a link please? The KMP matching algorithm is based on finite automata and works by implicitly building the transition table for an automaton that matches the string. Using a very clever linear-time preprocessing of the string to search for, a matching automaton can be constructed, and the automaton can then be simulated on the string to search in in linear time. The net

Given the following problem : Definition : Let S be a string over alphabet Σ . S' is the smallest period of S if S' is the smallest string such that : S = (S')^k (S'') , where S'' is a prefix of S . If no such S' exists , then S is not periodic . Example : S = abcabcabcabca . Then abcabc is a period since S = abcabc abcabc a , but the smallest period is abc since S = abc abc abc abc a . Give an algorithm to find the smallest period of input string S or declare that S is not periodic. Hint : You can do that in O(n) ... My solution : We use KMP , which runs in O(n) . By the definition of the