Fast and Flexible String Matching

The most important features of a string matching algorithm are its eeciency and its exibility. EEciency has traditionally received more attention, while exibility in the search pattern is becoming a more and more important issue. Most classical string matching algorithms are aimed at quickly nding an exact pattern in a text, being Knuth-Morris-Pratt (KMP) and the Boyer-Moore (BM) family the most famous ones. A recent development uses deterministic \suux automata" to design new optimal string matching algorithms, e.g. BDM and TurboBDM. Flexibility has been addressed quite separately by the use of \bit-parallelism", which simulates automata in their nondeterministic form by using bits and exploiting the intrinsic parallelism inside the computer word, e.g. the Shift-Or algorithm. Those algorithms are extended to handle classes of characters and errors in the pattern and/or in the text, their drawback being their inability to skip text characters. In this paper we merge bit-parallelism and suux automata, so that a nondetermin-istic suux automaton is simulated using bit-parallelism. The resulting algorithm, called BNDM, obtains the best from both worlds. It is much simpler to implement than BDM and nearly as simple as Shift-Or. It inherits from Shift-Or the ability to handle exible patterns and from BDM the ability to skip characters. BNDM is 30%-40% faster than BDM and up to 7 times faster than Shift-Or. When compared to the fastest existing algorithms on exact patterns (which belong to the BM family), BNDM is from 20% slower to 3 times faster, depending on the alphabet size. With respect to exible pattern searching, BNDM is by far the fastest technique to deal with classes of characters and is competitive to search allowing errors. In particular, BNDM seems very adequate for computational biology applications, since it is the fastest algorithm to search on DNA sequences and exible searching is an important problem in that area. As a theoretical development related to exible pattern matching, we introduce a new automaton to recognize suuxes of patterns with classes of characters. To the best of our knowledge, this automaton has not been studied before. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proot or direct commercial advantage and that copies show this notice on the rst page or initial screen of a display along with the full citation. Copyrights …