Related papers: Lower bounding edit distances between permutations

We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.

We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…

Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum…

We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…

Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…

The structure of all the permutations of a sequence can be represented as a permutohedron, a graph where vertices are permutations and two vertices are linked if a swap of adjacent elements in the permutation of one of the vertices produces…

We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields…

We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction applied to a permutation code. In particular, we show that a…

The study of genome rearrangement has many flavours, but they all are somehow tied to edit distances on variations of a multi-graph called the breakpoint graph. We study a weighted 2-break distance on Eulerian 2-edge-colored multi-graphs,…

In this paper, we introduce plane permutations, i.e. pairs $\mathfrak{p}=(s,\pi)$ where $s$ is an $n$-cycle and $\pi$ is an arbitrary permutation, represented as a two-row array. Accordingly a plane permutation gives rise to three distinct…

A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the…

We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier…

Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper…

Measuring the distance between two bacterial genomes under the inversion process is usually done by assuming all inversions to occur with equal probability. Recently, an approach to calculating inversion distance using group theory was…

We present a succinct data structure for permutation graphs, and their superclass of circular permutation graphs, i.e., data structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022),…

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…

In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…

A classical problem in comparative genomics is to compute the rearrangement distance, that is the minimum number of large-scale rearrangements required to transform a given genome into another given genome. While the most traditional…

We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with non-uniform cost. For arbitrary non-negative cost functions, we describe polynomial-time, constant-approximation decomposition…

In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an…