Order-Preserving Suffix Trees and Their Algorithmic Applications
Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Marcin Kubica, Alessio Langiu, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Tomasz Walen
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape" as a given pattern. These results include a linear-time order-preserving pattern matching algorithm for polynomially-bounded alphabet and an extension of this result to pattern matching with multiple patterns. We make one step forward in the analysis and give an $O(\frac{n\log{n}}{\log\log{n}})$ time randomized algorithm constructing suffix trees in the order-preserving setting. We show a number of applications of order-preserving suffix trees to identify patterns and repetitions in time series.
加权祖先问题是一个著名的推广的前身问题的树。已知如果$O(n\mathop{\mathrm{polylog}} n)$空间可用并且权重来自$[0..n]$，则查询需要$Ω(\log\log n)$时间，其中$n$是树节点的数量。然而，当应用于后缀树时，令人惊讶的是，该问题允许具有恒定查询时间的$O(n)$空间解决方案，如Gawrychowski，Lewenstein和Nicholson所示（Proc. ESA 2014）。这个问题的变体可以重新表述如下：给定一个字符串$s$的后缀树，我们需要一个数据结构，它可以在$O(1)$时间内在树中定位$s$的任何子串$s[p..q]$（就像一个人从根开始一路读$s[p..q]$）。不幸的是，Gawrychowski等人的数据结构没有有效的构造算法，限制了其作为算法工具的更广泛使用。在本文中，我们解决了这个问题，描述了一个数据结构的加权祖先后缀树与常数查询时间和线性构造算法。我们的解决方案是基于一种新的方法，使用所谓的不可约LCP值。
Computing Smallest Suffixient Arrays in Sublinear Time
Kyushu University（九州大学）；University of Chile（智利大学）；Center for Biotechnology and Bioengineering (CeBiB)（生物技术与生物工程中心）；University of Warsaw（华沙大学）；University of Palermo（巴勒莫大学）
Online Computation of Palindromes and Suffix Trees on Tries
Joint Graduate School of Mathematics for Innovation, Kyushu University（九州大学数学创新联合研究生院）；NTT Communication Science Laboratories（NTT通信科学实验室）；Department of Computer and Network Engineering, University of Electro-Communications（电子通信大学计算机与网络工程系）；Department of Informatics, Kyushu University（九州大学信息学系）；M&D Data Science Center, Institute of Integrated Research, Institute of Science Tokyo（东京科学大学综合研究研究所M&D数据科学中心）
Joint Graduate School of Mathematics for Innovation, Kyushu University（九州大学数学创新联合研究生院）；Department of Information Science and Technology, Kyushu University（九州大学信息科学技术系）；Graduate School of Informatics and Engineering, University of Electro-Communications（电波大学信息与工程学院）；Department of Informatics, Kyushu University（九州大学信息学系）
