A practical index for approximate dictionary matching with few mismatches

Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a surprisingly simple solution called a split index, which is based on the Dirichlet principle, for matching a keyword with few mismatches, and experimentally show that it offers competitive space-time tradeoffs. Our implementation in the C++ language is focused mostly on data compaction, which is beneficial for the search speed (e.g., by being cache friendly). We compare our solution with other algorithms and we show that it performs better for the Hamming distance. Query times in the order of 1 microsecond were reported for one mismatch for the dictionary size of a few megabytes on a medium-end PC. We also demonstrate that a basic compression technique consisting in $q$-gram substitution can significantly reduce the index size (up to 50% of the input text size for the DNA), while still keeping the query time relatively low

Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts

We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck

Efficient LZ78 factorization of grammar compressed text

We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string. Given an SLP of size $n$ representing a text $S$ of length $N$, our algorithm computes the LZ78 factorization of $T$ in $O(n\sqrt{N}+m\log N)$ time and $O(n\sqrt{N}+m)$ space, where $m$ is the number of resulting LZ78 factors. We also show how to improve the algorithm so that the $n\sqrt{N}$ term in the time and space complexities becomes either $nL$, where $L$ is the length of the longest LZ78 factor, or $(N - \alpha)$ where $\alpha \geq 0$ is a quantity which depends on the amount of redundancy that the SLP captures with respect to substrings of $S$ of a certain length. Since $m = O(N/\log_\sigma N)$ where $\sigma$ is the alphabet size, the latter is asymptotically at least as fast as a linear time algorithm which runs on the uncompressed string when $\sigma$ is constant, and can be more efficient when the text is compressible, i.e. when $m$ and $n$ are small.Comment: SPIRE 201

Prospects and limitations of full-text index structures in genome analysis

The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared

Sparse Representation of Astronomical Images

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on http://www.nonlinear-approx.info/examples/node1.htm