发表机构
University of Salerno（萨莱诺大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入逆Lyndon数组，通过下一个更大后缀数组与LCE修正项刻画，并基于最近后缀框架提出O(n)时间构建算法，同时用于线性时间重构规范逆Lyndon分解。
AI 中文摘要
Lyndon数组存储单词每个位置上从该位置开始的最长Lyndon因子的长度，在单词组合学中扮演重要角色，例如在构建后缀数组等基础数据结构时。本文引入逆Lyndon数组，即针对逆Lyndon单词的类似结构，逆Lyndon单词是指字典序大于其所有真非空后缀的单词。与标准Lyndon单词不同，逆Lyndon单词可能具有非平凡边界，这带来了真正的理论困难。我们证明逆Lyndon数组可以通过下一个更大后缀数组加上边界修正项来刻画，并证明该修正项等于最长公共扩展（LCE）值。基于此刻画，我们将Ellert线性时间构建Lyndon数组所依赖的最近后缀框架适配到逆设置，得到针对一般有序字母表的O(n)时间算法。最后，我们展示逆Lyndon数组还可用于在线性时间内重构规范逆Lyndon分解。
英文摘要
The Lyndon array stores, at each position of a word, the length of the longest Lyndon factor starting at that position and plays an important role in combinatorics on words, for example, in the construction of fundamental data structures such as the suffix array. In this paper, we introduce the Inverse Lyndon array, the analogous structure for inverse Lyndon words, namely words that are lexicographically greater than all their proper nonempty suffixes. Unlike standard Lyndon words, inverse Lyndon words may have non-trivial borders, which introduces a genuine theoretical difficulty. We show that the Inverse Lyndon array can be characterized in terms of the next greater suffix array together with a border-correction term, and we prove that this correction coincides with a longest common extension (LCE) value. Building on this characterization, we adapt the nearest-suffix framework underlying Ellert's linear-time construction of the Lyndon array to the inverse setting, obtaining an O(n)-time algorithm for general ordered alphabets. Finally, we show that the Inverse Lyndon array can also be used to reconstruct the canonical inverse Lyndon factorization in linear time.
Comments21 pages, no figures, SOFSEM conference
