String matching is the problem of finding all occurrences of a given pattern in a given text. It is an extensively studied problem in computer science because of its direct application to several areas such as text, image and signal processing, speech analysis and recognition, data compression, information retrieval, computational biology and chemistry. Since 1970 more than 85 string matching algorithms have been proposed, and more than 50% of them in the last ten years. In this paper we present Smart, an efficient and flexible tool designed for developing, testing, comparing and evaluating string matching algorithms. It also provides the most comprehensive survey of online exact single string matching algorithms together with a set of corpora available for testing purposes.

The String Matching Algorithms Research Tool.

Inverse Lyndon words and inverse Lyndon factorizations of words

We survey recent developments related to the Minimum Circuit Size Problem.

Language and Automata Theory and Applications, 14th International Conference LATA 2020, Milan, Italy, March 4–6, 2020, Proceedings

We present a simple and very efficient algorithm for string matching based on the combination of weak factor recognition and hashing. Despite its quadratic worst-case running time, our algorithm exhibits a sublinear behaviour. We also propose some practical improvements of our algorithm and a variant with a linear worst-case time complexity. Experimental results show that, in most cases, some of the variants of our algorithm obtain the best running times when compared, under various conditions, against the most effective algorithms present in the literature. For instance, in the case of small alphabets and long patterns, the gain in running time is up to 18%. This makes our proposed algorithm one of the most flexible solutions in practical cases.

Linear and Efficient String Matching Algorithms Based on Weak Factor Recognition

String matching is the problem of finding all the substrings of a text which correspond to a given pattern. It’s one of the most investigated problem in computer science, mainly due to its various applications in many fields. In recent years most solutions to the problem focused on efficiency and flexibility of the searching procedure and effective techniques appeared to speed-up previous solutions. In this paper we present a simple and very efficient algorithm for string matching. It can be seen as an extension of the Skip-Search algorithm to condensed alphabets with the aim of reducing the number of verifications during the searching phase. From our experimental results it turns out that the new variant obtains in most cases the best running time when compared against the most effective algorithms in literature. This makes the new algorithm one of the most flexible solutions in practical cases.

A Very Fast String Matching Algorithm Based on Condensed Alphabets

New bit-parallel algorithms for exact and approximate string matching are introduced. TSO is a two-way Shift-Or algorithm, TSA is a two-way Shift-And algorithm, and TSAdd is a two-way Shift-Add algorithm. Tuned Shift-Add is a minimalist improvement to the original Shift-Add algorithm. TSO and TSA are for exact string matching, while TSAdd and tuned Shift-Add are for approximate string matching with k mismatches. TSO and TSA are shown to be linear in the worst case and sublinear in the average case. Practical experiments show that the new algorithms are competitive with earlier algorithms.

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Improved Two-Way Bit-parallel Search

We present two variations of Duval's algorithm for computing the Lyndon factorization of a word. The first algorithm is designed for the case of small alphabets and is able to skip a significant portion of the characters of the string, for strings containing runs of the smallest character in the alphabet. Experimental results show that it is faster than Duval's original algorithm, more than ten times in the case of long DNA strings. The second algorithm computes, given a run-length encoded string $R$ of length $\rho$, the Lyndon factorization of $R$ in $O(\rho)$ time and constant space.

Alternative algorithms for Lyndon factorization.

We consider the problem of jumbled matching where the objective is to find all permuted occurrences of a pattern in a text. Besides exact matching we study approximate matching where each occurrence is allowed to contain at most k wrong or superfluous characters. We present online algorithms applying bit-parallelism to both types of jumbled matching. Most of our algorithms are variations of earlier algorithms. We show by practical experiments that our algorithms are competitive with the previous solutions.

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Tuning Algorithms for Jumbled Matching

Alternative Algorithms for Lyndon Factorization

Jumbled pattern matching addresses the problem of finding all permuted occurrences of a substring in a text. We introduce two improved algorithms for exact jumbled matching of short patterns. Our solutions apply SIMD (Single Instruction Multiple Data) computation in order to quickly filter the text. One of them utilizes the equal any operation and the other searches for the least frequent character of the pattern. Our experiments show that the best algorithm is 30% faster than previous algorithms for short English patterns.

Sukhpal Singh Ghuman

Papers

Improved Two-Way Bit-parallel Search

Alternative algorithms for Lyndon factorization.

Tuning Algorithms for Jumbled Matching

Alternative Algorithms for Lyndon Factorization

Jumbled matching with SIMD