Related papers: A New Algebraic Approach for String Reconstruction…

A factorization $f_1, \ldots, f_m$ of a string $w$ of length $n$ is called a repetition factorization of $w$ if $f_i$ is a repetition, i.e., $f_i$ is a form of $x^kx'$, where $x$ is a non-empty string, $x'$ is a (possibly-empty) proper…

In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation…

Cadences are structurally maximal arithmetic progressions of indices corresponding to equal characters in an underlying string. This paper provides a polynomial time detection algorithm for 3-cadences in grammar-compressed binary strings.…

We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns…

This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

String matching algorithm plays the vital role in the Computational Biology. The functional and structural relationship of the biological sequence is determined by similarities on that sequence. For that, the researcher is supposed to aware…

Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $\Sigma$, where $s$ and $t$ are positive integers. The longest common subsequence and substring problem for multiple strings $X_1, X_2, ..., X_s$ and $Y_1, Y_2,…

This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust…

An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…

In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…

The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…

We give a polynomial time algorithm for the lossy population recovery problem. In this problem, the goal is to approximately learn an unknown distribution on binary strings of length $n$ from lossy samples: for some parameter $\mu$ each…

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string…

In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings $A$ and $B$. More recently, a set of four constrained LCS problems (called generalized…

We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node $t$ in a given tree $T$. Upon querying a node $v$ of the tree, the strategy receives as a reply an…

Disentangled distributed representations of data are desirable for machine learning, since they are more expressive and can generalize from fewer examples. However, for complex data, the distributed representations of multiple objects…

We show how, given a straight-line program with $g$ rules for a binary string $B$ of length $n$, in $O(g^{2 / 3} n^{4 / 3})$ time we can build a linear-space index such that, given $m$ and $c$, in O(1) time we can determine whether there is…