Question

What are the main differences between the Knuth-Morris-Pratt search algorithm and the Boyer-Moore search algorithm?

I know KMP searches for Y in X, trying to define a pattern in Y, and saves the pattern in a vector. I also know that BM works better for small words, like DNA (ACTG).

What are the main differences in how they work? Which one is faster? Which one is less computer-greedy? In which cases?

Answer 1

Moore’s UTexas webpage walks through both algorithms in a step-by-step fashion (he also provides various technical sources):

• Knuth-Morris-Pratt
• Boyer-Moore

According to the man himself,

The classic Boyer-Moore algorithm suffers from the phenomenon that it
tends not to work so efficiently on small alphabets like DNA. The skip
distance tends to stop growing with the pattern length because
substrings re-occur frequently. By remembering more of what has
already been matched, one can get larger skips through the text. One
can even arrange “perfect memory” and thus look at each character at
most once, whereas the Boyer-Moore algorithm, while linear, may
inspect a character from the text multiple times. This idea of
remembering more has been explored in the literature by others. It
suffers from the need for very large tables or state machines.

However, there have been some modifications of BM that have made small-alphabet searching viable.