Related papers: The complexity of string partitioning

Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…

Minimizers are sampling schemes with numerous applications in computational biology. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a linear order $\rho$ on strings of length $k$ (also…

In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set $X$ of species from a multiset $\Pi$ of partitions corresponding to various attributes of these species. One approach that is used to…

Minimizer schemes, or just minimizers, are a very important computational primitive in sampling and sketching biological strings. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a total order…

Let P be a planar n-point set. A k-partition of P is a subdivision of P into n/k parts of roughly equal size and a sequence of triangles such that each part is contained in a triangle. A line is k-shallow if it has at most k points of P…

We consider the problem of finding a minimum common partition of two strings (MCSP). The problem has its application in genome comparison. MCSP problem is proved to be NP-hard. In this paper, we develop an Integer Programming (IP)…

Computing an optimal chain of fragments is a classical problem in string algorithms, with important applications in computational biology. There exist two efficient dynamic programming algorithms solving this problem, based on different…

Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…

The cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least…

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…

We develop a theory of k-partitions of the set of infinite words recognizable by classes of finite automata. The theory enables to complete proofs of existing results about topological classifications of the (aperiodic) omega-regular…

In the Shortest Superstring problem we are given a set of strings $S=\{s_1, \ldots, s_n\}$ and integer $\ell$ and the question is to decide whether there is a superstring $s$ of length at most $\ell$ containing all strings of $S$ as…

Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…

With our current level of understanding, the problem of making string theory predictions is not one of "solving" the theory, but rather of trying to determine whether there are any generic expectations. Within this context, we discuss what…

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…

Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…

We define entanglement entropy in string perturbation theory using the orbifold method -- a stringy analog of the replica method in field theory. To this end, we use the Newton series to analytically continue in $N$ the partition functions…

We use integrability to construct the general classical splitting string solution on R x S^3. Namely, given any incoming string solution satisfying a necessary self-intersection property at some given instant in time, we use the…

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a…

The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text). A matching is an order-preserving embedding of P into T. In the Generalized Permutation Pattern…