Sorting by Prefix Block-Interchanges

Regular Languages meet Prefix Sorting

Indexing strings via prefix (or suffix) sorting is, arguably, one of the most successful algorithmic techniques developed in the last decades. Can indexing be extended to languages? The main contribution of this paper is to initiate the study of the sub-class of regular languages accepted by an automaton whose states can be prefix-sorted. Starting from the recent notion of Wheeler graph [Gagie et al., TCS 2017]-which extends naturally the concept of prefix sorting to labeled graphs-we investigate the properties of Wheeler languages, that is, regular languages admitting an accepting Wheeler fin…

确定性有限自动机的更快前缀排序算法

Faster Prefix-Sorting Algorithms for Deterministic Finite Automata

本文研究DFA的最小宽度偏反词典序计算，利用新组合性质提出任意DFA的$O(mn)$、$O(n^2\log n)$排序算法及无环DFA的$O(m\log n)$算法，并验证其实用性。

Log-Lists and Their Applications to Sorting by Transpositions, Reversals and Block-Interchanges

Link-cut trees have been introduced by D.D. Sleator and R.E. Tarjan (Journal of Computer and System Sciences, 1983) with the aim of efficiently maintaining a forest of vertex-disjoint dynamic rooted trees under cut and link operations. These operations respectively disconnect a subtree from a tree, and join two trees by an edge. Additionally, link-cut trees allow to change the root of a tree and to perform a number of updates and queries on cost values defined on the arcs of the trees. All these operations are performed in $O(\log\, n)$ amortized or worst-case time, depending on the implementa…

前缀排序确定有限自动机（DFAs）：一种递归算法

Prefix Sorting DFAs: a Recursive Algorithm

本文受Farach后缀树构建算法启发，提出一种$O(n^2)$时间复杂度的递归算法，改进了DFA后缀数组的构建时间界，并深化了对图的字典序与组合结构的理解，助力图后缀树构建这一长期开放问题的研究。

LCP-Aware Parallel String Sorting

When lexicographically sorting strings, it is not always necessary to inspect all symbols. For example, the lexicographical rank of "europar" amongst the strings "eureka", "eurasia", and "excells" only depends on its so called relevant prefix "euro". The distinguishing prefix size $D$ of a set of strings is the number of symbols that actually need to be inspected to establish the lexicographical ordering of all strings. Efficient string sorters should be $D$-aware, i.e. their complexity should depend on $D$ rather than on the total number $N$ of all symbols in all strings. While there are many…

前缀共享是一个排序问题

Prefix Sharing Is a Sorting Problem

本文证明LLM服务中前缀共享的片段排序问题等价于在请求上选择二叉层次结构，提出O(3^m)精确算法和1/2近似凝聚聚类，在BEIR上减少17-36%预填充。

Polynomial-time sortable stacks of burnt pancakes

Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that case not only reverse the order of elements but also invert their signs. Although three decades have now passed since the first works on these problems, neither their computational complexity nor the maxim…

Lower bounding edit distances between permutations

A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in "as few moves as possible", using a given set of allowed operations, or computing the number of moves the sorting process requires, often referred to as the \emph{distance} of the permutation. These operations often act on just one or two segments of the permutation, e.g. by reversing one segment or exchanging two segments. The \emph{cycle graph} of the permutation to sort is a fundamental tool in the theory of genome rearrange…

Permutree 排序

Permutree sorting

本文提出 permutree 排序，将栈排序与 $c$-排序推广到由不相交集合 $U,D$ 参数化的排列排序，并用自动机刻画可排序性和约化表达式。

PivotCompress: Compression by Sorting

Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed recursively. The sorted permutation can be specified by recording the decisions made by quicksort. If the size of the data is known, then the quicksort decisions describe the data at a rate that is nearly as efficient as the minimal prefix-free code for the distribution, which is bounded by the entropy of the distribution. This is possible even though the distributi…