Related papers: Reconstruction of hypermatrices from subhypermatri…

The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required…

$\newcommand{\Re}{\mathbb{R}}$We study the minWSPD problem of computing the minimum-size well-separated pairs decomposition of a set of points, and show constant approximation algorithms in low-dimensional Euclidean space and doubling…

We study the formula complexity of Iterated Sub-Permutation Matrix Multiplication, the logspace-complete problem of computing the product of $k$ $n$-by-$n$ Boolean matrices with at most a single $1$ in each row and column. For all $d \le…

We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees…

This study investigates whether reoptimization can help in solving the closest substring problem. We are dealing with the following reoptimization scenario. Suppose, we have an optimal l-length closest substring of a given set of sequences…

The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…

We consider the algorithmic problem of generating each subset of $[n]:=\{1,2,\ldots,n\}$ whose size is in some interval $[k,l]$, $0\leq k\leq l\leq n$, exactly once (cyclically) by repeatedly adding or removing a single element, or by…

In the Feedback Vertex Set problem, one is given an undirected graph $G$ and an integer $k$, and one needs to determine whether there exists a set of $k$ vertices that intersects all cycles of $G$ (a so-called feedback vertex set). Feedback…

In this paper we provide an elementary and easy proof that a proper subalgebra of the matrix algebra $ \mathbb{K}^{n,n }$, with $n \geq3$ and $\mathbb{K}$ an arbitrary field, has dimension strictly less than $n^2-1$.

Given natural numbers $k \leq s \leq n$, we ask: what is the minimal VC-dimension of a family $\mathcal{F}$ of $s$-subsets of $[n]$ that covers all $k$-subsets of $[n]$? We first show that for sufficiently large $n$ this number is always…

An $(n, k, d, \alpha)$-MSR (minimum storage regeneration) code is a set of $n$ nodes used to store a file. For a file of total size $k\alpha$, each node stores $\alpha$ symbols, any $k$ nodes recover the file, and any $d$ nodes can repair…

\textsc{Densest $k$-Subgraph} is the problem to find a vertex subset $S$ of size $k$ such that the number of edges in the subgraph induced by $S$ is maximized. In this paper, we show that \textsc{Densest $k$-Subgraph} is fixed parameter…

The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance…

A permutation $\sigma\in S_n$ is said to be $k$-universal or a $k$-superpattern if for every $\pi\in S_k$, there is a subsequence of $\sigma$ that is order-isomorphic to $\pi$. A simple counting argument shows that $\sigma$ can be a…

We consider the problem of designing optimal $M \times N$ ($M \leq N$) sensing matrices which minimize the maximum condition number of all the submatrices of $K$ columns. Such matrices minimize the worst-case estimation errors when only $K$…

The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the minimum independence number of a tree decomposition of it.…

The central problem in sequence reconstruction is to find the minimum number of distinct channel outputs required to uniquely reconstruct the transmitted sequence. According to Levenshtein's work in 2001, this number is determined by the…

The goal of the trace reconstruction problem is to recover a string $x\in\{0,1\}^n$ given many independent {\em traces} of $x$, where a trace is a subsequence obtained from deleting bits of $x$ independently with some given probability…

We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result…

For an $n \times n$ matrix $M$ with entries in $\mathbb{Z}_2$ denote by $R(M)$ the minimal rank of all the matrices obtained by changing some numbers on the main diagonal of $M$. We prove that for each non-negative integer $k$ there is a…