Related papers: Lower bounding edit distances between permutations

We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…

Genome rearrangements can be modeled as $k$-breaks, which break a genome at k positions and glue the resulting fragments in a new order. In particular, reversals, translocations, fusions, and fissions are modeled as $2$-breaks, and…

We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked…

A cyclic permutation $\pi:\{1, \dots, N\}\to \{1, \dots, N\}$ has a \emph{block structure} if there is a partition of $\{1, \dots, N\}$ into $k\notin\{1,N\}$ segments (\emph{blocks}) permuted by $\pi$; call $k$ the \emph{period} of this…

Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact…

A new lower bound on the minimum Hamming distance of linear quasi-cyclic codes over finite fields is proposed. It is based on spectral analysis and generalizes the Semenov- Trifonov bound in a similar way as the Hartmann-Tzeng bound extends…

Normal approximations for descents and inversions of permutations of the set $\{1,2,...,n\}$ are well known. A number of sequences that occur in practice, such as the human genome and other genomes, contain many repeated elements. Motivated…

Any permutation in the finite symmetric group can be written as a product of simple transpositions $s_i = (i~i+1)$. For a fixed permutation $\sigma \in \mathfrak{S}_n$ the products of minimal length are called reduced decompositions or…

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…

Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation…

We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for…

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…

Motivation: Genome rearrangement plays an important role in evolutionary biology and has profound impacts on phenotype in organisms ranging from microbes to humans. The mechanisms for genome rearrangement events remain unclear. Lots of…

In a seminal paper of Charikar et al.~on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors. Here we improve the lower bound for the famous {\sf RePair}…

Recall that an excedance of a permutation $\pi$ is any position $i$ such that $\pi_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it…

We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain,…

Motivated by the problem of redistricting, we study area-preserving reconfigurations of connected subdivisions of a simple polygon. A connected subdivision of a polygon $\mathcal{R}$, called a district map, is a set of interior disjoint…

Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…

It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We…

The graph edit distance is an intuitive measure to quantify the dissimilarity of graphs, but its computation is NP-hard and challenging in practice. We introduce methods for answering nearest neighbor and range queries regarding this…