Rabin-Karp Algorithm

• Let characters be digits in radix- notation.
• Choose a prime number q such that fits within a computer word to speed computations.
  
• Algorithm:
  Compute (P mod q)
  Compute (T[s+1, .., s+m] mod q) for s = 0 .. n-m
  Test against P only those sequences in T having the same (mod q) value
• (T[s+1, .., s+m] mod q) can be incrementally computed by subtracting the high-order digit, shifting, adding the low-order bit, all in modulo q arithmetic.

Example

$\Sigma$ = {0, 1, .., 9}

P = 12, P mod 3 = 0

q = 3