Heikki Hyyrö

Faster Bit-Parallel Approximate String Matching

We present a new bit-parallel technique for approximate string matching. We build on two previous techniques. The first one [Myers, J. of the ACM, 1999], searches for a pattern of length m in a text of length n permitting k differences in O(mn/w) time, where w is the width of the computer word. The second one [Navarro and Raffinot, ACM JEA, 2000], extends a sublinear-time exact algorithm to approximate searching. The latter technique makes use of an O(kmn/w) time algorithm [Wu and Manber, Comm. ACM, 1992] for its internal workings. This algorithm is slow but flexible enough to support all the required operations. In this paper we show that the faster algorithm of Myers can be adapted to support all those operations. This involves extending it to compute edit distance, to search for any pattern suffix, and to detect in advance the impossibility of a later match. The result is an algorithm that performs better than the original version of Navarro and Raffinot and that is the fastest for several combinations of m, k and alphabet sizes that are useful, for example, in natural language searching and computational biology.

Increased bit-parallelism for approximate and multiple string matching

Bit-parallelism permits executing several operations simultaneously over a set of bits or numbers stored in a single computer word. This technique permits searching for the approximate occurrences of a pattern of length <i>m</i> in a text of length <i>n</i> in time <i>O</i>(⌈<i>m</i>/<i>w</i>⌉<i>n</i>), where <i>w</i> is the number of bits in the computer word. Although this is asymptotically the optimal bit-parallel speedup over the basic <i>O</i>(<i>mn</i>) time algorithm, it wastes bit-parallelisms power in the common case where <i>m</i> is much smaller than <i>w</i>, since <i>w</i>−<i>m</i> bits in the computer words are unused. In this paper, we explore different ways to increase the bit-parallelism when the search pattern is short. First, we show how multiple patterns can be packed into a single computer word so as to search for all them simultaneously. Instead of spending <i>O</i>(<i>rn</i>) time to search for <i>r</i> patterns of length <i>m</i>≤<i>w</i>/2, we need <i>O</i>(⌈<i>rm</i>/<i>w</i>⌉<i>n</i>) time. Second, we show how the mechanism permits boosting the search for a single pattern of length <i>m</i>≤<i>w</i>/2, which can be searched for in <i>O</i>(⌈<i>n</i>/⌊<i>w</i>/<i>m</i>⌋⌉) bit-parallel steps instead of <i>O</i>(<i>n</i>). Third, we show how to extend these algorithms so that the time bounds essentially depend on <i>k</i> instead of <i>m</i>, where <i>k</i> is the maximum number of differences permitted. Finally, we show how the ideas can be applied to other problems such as multiple exact string matching and one-against-all computation of edit distance and longest common subsequences. Our experimental results show that the new algorithms work well in practice, obtaining significant speedups over the best existing alternatives, especially on short patterns and moderate number of differences allowed. This work fills an important gap in the field, where little work has focused on very short patterns.

Bit-Parallel Witnesses and Their Applications to Approximate String Matching

Abstract We present a new bit-parallel technique for approximate string matching. We build on two previous techniques. The first one, BPM (Myers, 1999), searches for a pattern of length m in a text of length n permitting k differences in

Increased Bit-Parallelism for Approximate String Matching

O(\lceil m/w \rceil n)

Finding Optimal Pairs of Cooperative and Competing Patterns with Bounded Distance

time, where w is the width of the computer word. The second one, ABNDM (Navarro and Raffinot, 2000), extends a sublinear-time exact algorithm to approximate searching. ABNDM relies on another algorithm, BPA (Wu and Manber, 1992), which makes use of an

Finding Optimal Pairs of Patterns

O(k \lceil m/w \rceil n)

Bit-parallel approximate string matching algorithms with transposition

time algorithm for its internal workings. BPA is slow but flexible enough to support all operations required by ABNDM. We improve previous ABNDM analyses, showing that it is average-optimal in number of inspected characters, although the overall complexity is higher because of the

Improving the bit-parallel NFA of Baeza-Yates and Navarro for approximate string matching

O(k \lceil m/w \rceil )

An Efficient Linear Space Algorithm for Consecutive Suffix Alignment under Edit Distance (Short Preliminary Paper)

work done per inspected character. We then show that the faster BPM can be adapted to support all the operations required by ABNDM. This involves extending it to compute edit distance, to search for any pattern suffix, and to detect in advance the impossibility of a later match. The solution to those challenges is based on the concept of a witness, which permits sampling some dynamic programming matrix values to bound, deduce or compute others fast. The resulting algorithm is average-optimal for m ≤ w, assuming the alphabet size is constant. In practice, it performs better than the original ABNDM and is the fastest algorithm for several combinations of m, k and alphabet sizes that are useful, for example, in natural language searching and computational biology. To show that the concept of witnesses can be used in further scenarios, we also improve a recent variant of BPM. The use of witnesses greatly improves the running time of this algorithm too.

Fast bit-vector algorithms for approximate string matching under indel distance

Bit-parallelism permits executing several operations simultaneously over a set of bits or numbers stored in a single computer word. This technique permits searching for the approximate occurrences of a pattern of length m in a text of length n in time O(⌈m/w⌉n), where w is the number of bits in the computer word. Although this is asymptotically the optimal speedup over the basic O(mn) time algorithm, it wastes bit-parallelism’s power in the common case where m is much smaller than w, since w-m bits in the computer words get unused.