Related papers: On Tuning the Bad-Character Rule: the Worst-Charac…
We propose a very simple randomised data structure that stores an approximation from above of a lattice-valued function. Computing the function value requires a constant number of steps, and the error probability can be balanced with space…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest…
I consider the problem of classifying individual behavior in a simple setting of outcome performativity where the behavior the algorithm seeks to classify is itself dependent on the algorithm. I show in this context that the most accurate…
Machine learning has been widely applied in many aspects, but training a machine learning model is increasingly difficult. There are more optimization problems named "black-box" where the relationship between model parameters and outcomes…
Given a pattern x of length m and a text y of length n, both over an ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. It is an…
We present a new efficient method for approximate search in electronic lexica. Given an input string (the pattern) and a similarity threshold, the algorithm retrieves all entries of the lexicon that are sufficiently similar to the pattern.…
Given a set of patterns called a dictionary and a text, the dictionary matching problem is a task to find all occurrence positions of all patterns in the text. The dictionary matching problem can be solved efficiently by using the…
String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm at hand requires to employ the operators in a specific order. Sequential orderings are well-known and a simultaneous…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…
The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet…
Considering two optimally aligned random sequences, we investigate the effect on the alignment score caused by changing a random letter in one of the two sequences. Using this idea in conjunction with large deviations theory, we show that…
The problem of optical character recognition, OCR, has been widely discussed in the literature. Having a hand-written text, the program aims at recognizing the text. Even though there are several approaches to this issue, it is still an…
Neural machine translation (NMT), a new approach to machine translation, has been proved to outperform conventional statistical machine translation (SMT) across a variety of language pairs. Translation is an open-vocabulary problem, but…
Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time…
We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…