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At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings $A$ and $B$ and a…
This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not…
Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…
In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…
We consider labeled directed graphs where each vertex is labeled with a non-empty string. Such labeled graphs are also known as non-linear texts in the literature. In this paper, we introduce a new problem of comparing two given labeled…
Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence. If $\ell$ is the length of the overlap, we prove that the expected…
Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges…
We consider two independent binary i.i.d. random strings $X$ and $Y$ of equal length $n$ and the optimal alignments according to a symmetric scoring functions only. We decompose the space of scoring functions into five components. Two of…
A weighted string over an alphabet of size $\sigma$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences,…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
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…
A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…
In the Shortest Common Superstring problem (SCS), one needs to find the shortest superstring for a set of strings. While SCS is NP-hard and MAX-SNP-hard, the Greedy Algorithm "choose two strings with the largest overlap; merge them; repeat"…
The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Sigma. It is well-known that its decision version denoted [SR8] in [Garey and…
In the problem of the longest common substring with $k$ mismatches we are given two strings $X, Y$ and must find the maximal length $\ell$ such that there is a length-$\ell$ substring of $X$ and a length-$\ell$ substring of $Y$ that differ…
Let $(X_i)_{i \geq 1}$ and $(Y_i)_{i\geq1}$ be two independent sequences of independent identically distributed random variables taking their values in a common finite alphabet and having the same law. Let $LC_n$ be the length of the…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $\alpha \le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold…