A new problem in string searching

We describe a substring search problem that arises in group presentation simplification processes. We suggest a two-level searching model: skip and match levels. We give two timestamp algorithms which skip searching parts of the text where there are no matches at all and prove their correctness. At the match level, we consider Harrison signature, Karp-Rabin fingerprint, Bloom filter and automata based matching algorithms and present experimental performance figures.Comment: To appear in Proceedings Fifth Annual International Symposium on Algorithms and Computation (ISAAC'94), Lecture Notes in Computer Scienc

From Regular Expression Matching to Parsing

Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular expression parsing makes finding matches of a regular expression even more useful by allowing us to directly extract subpatterns of the match, e.g., for extracting IP-addresses from internet traffic analysis or extracting subparts of genomes from genetic data bases. We present a new general techniques for efficiently converting a large class of algorithms that determine if a string $Q$ matches regular expression $R$ into algorithms that can construct a corresponding mapping. As a consequence, we obtain the first efficient linear space solutions for regular expression parsing

Random Access to Grammar Compressed Strings

Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string. Let $S$ be a string of length $N$ compressed into a context-free grammar $\mathcal{S}$ of size $n$. We present two representations of $\mathcal{S}$ achieving $O(\log N)$ random access time, and either $O(n\cdot \alpha_k(n))$ construction time and space on the pointer machine model, or $O(n)$ construction time and space on the RAM. Here, $\alpha_k(n)$ is the inverse of the $k^{th}$ row of Ackermann's function. Our representations also efficiently support decompression of any substring in $S$: we can decompress any substring of length $m$ in the same complexity as a single random access query and additional $O(m)$ time. Combining these results with fast algorithms for uncompressed approximate string matching leads to several efficient algorithms for approximate string matching on grammar-compressed strings without decompression. For instance, we can find all approximate occurrences of a pattern $P$ with at most $k$ errors in time $O(n(\min\{|P|k, k^4 + |P|\} + \log N) + occ)$, where $occ$ is the number of occurrences of $P$ in $S$. Finally, we generalize our results to navigation and other operations on grammar-compressed ordered trees. All of the above bounds significantly improve the currently best known results. To achieve these bounds, we introduce several new techniques and data structures of independent interest, including a predecessor data structure, two "biased" weighted ancestor data structures, and a compact representation of heavy paths in grammars.Comment: Preliminary version in SODA 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