Related papers: Sorting by Prefix Block-Interchanges

We construct a refined bijection $\phi$ between alternating permutations and 0-1-2 increasing trees with degree at most 2. It satisfies that the first element of alternating permutation $\pi$ is equal to the first vertex in $\phi(\pi)$ in…

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…

The poset of permutations of [n] under Bruhat ordering is studied. We give nontrivial upper and lower bounds for the number of comparable pairs of permutations in both the weak and strong versions of this order. In light of numerical…

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet…

This paper focuses on waveform design for joint radar and communication systems and presents a new subset selection process to improve the communication error rate performance and global accuracy of radar sensing of the random stepped…

A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…

The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the…

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…

We propose a method for constructing optimal block designs for experiments on networks. The response model for a given network interference structure extends the linear network effects model to incorporate blocks. The optimality criteria…

This paper proposes a new algorithm for generating all permutations of multisets. The method uses transpositions only and adjacent transpositions are favoured. The algorithm requires a strong homogeneous transposition condition:…

A novel paradigm for sorting is introduced, based upon resetting. Using simple examples, we demonstrate that sorting is achieved by resetting the velocity component(s) or orientation of the particles, rather than position. The objects to be…

Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck…

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…

We investigate the relation between bifix codes and interval exchange transformations. We prove that the class of natural codings of regular interval echange transformations is closed under maximal bifix decoding.

We consider avoidance of permutation patterns with designated gap sizes between pairs of consecutive letters. We call the patterns having such constraints distant patterns (DPs) and we show their relation to other pattern notions…

In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…

Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which…

Let $k$ be a nonnegative integer, and let $\alpha$ and $\beta$ be two permutations of $n$ symbols. We say that $\alpha$ and $\beta$ $k$-commute if $H(\alpha\beta, \beta\alpha)=k$, where $H$ denotes the Hamming metric between permutations.…

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…

Fine-tuning is the de facto way to leverage large pretrained language models to perform downstream tasks. However, it modifies all the language model parameters and therefore necessitates storing a full copy for each task. In this paper, we…