Related papers: The Sequence Reconstruction of Permutations under …

Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…

An $[n,k]$ code $\mathcal{C}$ is said to be locally recoverable in the presence of a single erasure, and with locality parameter $r$, if each of the $n$ code symbols of $\mathcal{C}$ can be recovered by accessing at most $r$ other code…

For non-negative integer parameters $r,u,m,n$ define \begin{align*} \cal{D}(r,u,m,n) := \big\{\ \sigma\in \cal{S}_{r+n}\ \big|\ \sigma(x)=y \textrm{ for exactly } u \textrm{ pairs } (x,y) \textrm{ such that } 1\leq x,y\leq r \textrm{ and }…

This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset…

Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…

In the well-known complexity class NP are combinatorial problems, whose optimization counterparts are important for many practical settings. These problems typically consider full knowledge about the input. In practical settings, however,…

Reconstructing a signal on a graph from noisy observations of a subset of the vertices is a fundamental problem in the field of graph signal processing. This paper investigates how sample size affects reconstruction error in the presence of…

In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for…

Let $S_{\rm lcm}(n)$ denote the set of permutations $\pi$ of $[n]=\{1,2,\dots,n\}$ such that ${\rm lcm}[j,\pi(j)]\le n$ for each $j\in[n]$. Further, let $S_{\rm div}(n)$ denote the number of permutations $\pi$ of $[n]$ such that…

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Let us say that an element of a given family $\A$ of subsets of $\R^d$ can be reconstructed using $n$ test sets if there exist $T_1,...,T_n \subset \R^d$ such that whenever $A,B\in \A$ and the Lebesgue measures of $A \cap T_i$ and $B \cap…

Superpermutations are words over a finite alphabet containing every permutation as a factor. Finding the minimal length of a superpermutation is still an open problem. In this article, we introduce superpermutations matrices. We establish a…

Several new applications and a number of new mathematical techniques have increased the research on error-correcting codes in the Lee metric in the last decade. In this work we consider several coding problems and constructions of…

Let $S_n$ be the symmetric group on the set $[n]:=\{1,2,\ldots,n\}$. Given a permutation $\sigma=\sigma_1\sigma_2 \cdots \sigma_n \in S_n$, we say it has a descent at index $i$ if $\sigma_i>\sigma_{i+1}$. Let $\mathcal{D}(\sigma)$ be the…

We study recovering a 1D order from a noisy, locally sampled pairwise comparison matrix under a tight query budget. We recast the task as reconstructing a sparse, noisy line graph and present, to our knowledge, the first method that…

We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern $P[1 .. m]$ on a large repetitive text collection $T[1 .. n]$, which is represented as a (hopefully much smaller) run-length context-free grammar of…

The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…

Nanopore sequencing is a promising technology for DNA sequencing. In this paper, we investigate a specific model of the nanopore sequencer, which takes a $q$-ary sequence of length $n$ as input and outputs a vector of length $n+\ell-1$…

Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…