Faster Approximate String Matching for Short Patterns

We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have lengths $m$ and $n$, respectively. On a standard unit-cost word RAM with word size $w \geq \log n$ we present an algorithm using time $$O(nk \cdot \min(\frac{\log^2 m}{\log n},\frac{\log^2 m\log w}{w}) + n)$$ When $P$ is short, namely, $m = 2^{o(\sqrt{\log n})}$ or $m = 2^{o(\sqrt{w/\log w})}$ this improves the previously best known time bounds for the problem. The result is achieved using a novel implementation of the Landau-Vishkin algorithm based on tabulation and word-level parallelism.Comment: To appear in Theory of Computing System

An efficient algorithm for generating super condensed neighborhoods

Abstract. Indexing methods for the approximate string matching problem spend a considerable effort generating condensed neighborhoods. Here, we point out that condensed neighborhoods are not a minimal representation of a pattern neighborhood. We show that we can restrict our attention to super condensed neighborhoods which are minimal. We then present an algorithm for generating Super Condensed Neighborhoods. The algorithm runs in O(m⌈m/w⌉s), where m is the pattern size, s is the size of the super condensed neighborhood and w the size of the processor word. Previous algorithms took O(m⌈m/w⌉c) time, where c is the size of the condensed neighborhood. We further improve this algorithm by using Bit-Parallelism and Increased Bit-Parallelism techniques. Our experimental results show that the resulting algorithm is very fast.

A Practical Index for Genome Searching

Current search tools for computational biology trade e#- ciency for precision, losing many relevant matches. We push in the direction of obtaining maximum e#ciency from an indexing scheme that does not lose any relevant match. We show that it is feasible to search the human genome e#ciently on an average desktop computer