Breaking the Cubic Barrier for (Unweighted) Tree Edit Distance

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2023-11-16 DOI:10.1137/22m1480719

Xiao Mao

{"title":"Breaking the Cubic Barrier for (Unweighted) Tree Edit Distance","authors":"Xiao Mao","doi":"10.1137/22m1480719","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Computing, Ahead of Print. <br/> Abstract. The (unweighted) tree edit distance problem for [math] node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in [math] time [Demaine et al., Automata, Languages and Programming, Springer, Berlin, 2007, pp. 146–157]. The same paper also showed that [math] is the best possible running time for any algorithm using the so-called decomposition strategy, which underlies almost all the known algorithms for this problem. These algorithms would also work for the weighted tree edit distance problem, which cannot be solved in truly subcubic time under the All-Pairs Shortest Paths conjecture [Bringmann et al., ACM Trans. Algorithms, 16 (2020), pp. 48:1–48:22]. In this paper, we break the cubic barrier by showing an [math] time algorithm for the unweighted tree edit distance problem. We consider an equivalent maximization problem and use a dynamic programming scheme involving matrices with many special properties. By using a decomposition scheme as well as several combinatorial techniques, we reduce tree edit distance to the max-plus product of bounded-difference matrices, which can be solved in truly subcubic time [Bringmann et al., Proceedings of the IEEE 57th Annual Symposium on Foundations of Computer Science, 2016, pp. 375–384].","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"59 5","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1137/22m1480719","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

Abstract

SIAM Journal on Computing, Ahead of Print.
Abstract. The (unweighted) tree edit distance problem for [math] node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in [math] time [Demaine et al., Automata, Languages and Programming, Springer, Berlin, 2007, pp. 146–157]. The same paper also showed that [math] is the best possible running time for any algorithm using the so-called decomposition strategy, which underlies almost all the known algorithms for this problem. These algorithms would also work for the weighted tree edit distance problem, which cannot be solved in truly subcubic time under the All-Pairs Shortest Paths conjecture [Bringmann et al., ACM Trans. Algorithms, 16 (2020), pp. 48:1–48:22]. In this paper, we break the cubic barrier by showing an [math] time algorithm for the unweighted tree edit distance problem. We consider an equivalent maximization problem and use a dynamic programming scheme involving matrices with many special properties. By using a decomposition scheme as well as several combinatorial techniques, we reduce tree edit distance to the max-plus product of bounded-difference matrices, which can be solved in truly subcubic time [Bringmann et al., Proceedings of the IEEE 57th Annual Symposium on Foundations of Computer Science, 2016, pp. 375–384].

查看原文本刊更多论文

打破(未加权)树编辑距离的立方体障碍

SIAM计算机杂志，出版前。摘要。[math]节点树的(未加权的)树编辑距离问题要求计算两个带有节点标签的根树之间的不相似性度量。目前最好的算法是十多年前的[数学]时间[Demaine et al.， Automata, Languages and Programming, Springer, Berlin, 2007, pp. 146-157]。同一篇论文还表明，对于使用所谓的分解策略的任何算法来说，[math]是可能的最佳运行时间，这是几乎所有已知算法解决该问题的基础。这些算法也适用于加权树编辑距离问题，该问题在全对最短路径猜想下无法在真正的次立方时间内解决[Bringmann等人，ACM Trans.]。算法，16 (2020)，pp. 48:1-48:22]。在本文中，我们通过展示一种[数学]时间算法来解决未加权树编辑距离问题，从而打破了三次障碍。我们考虑了一个等价最大化问题，并使用了一个包含许多特殊性质矩阵的动态规划方案。通过使用分解方案和几种组合技术，我们将树编辑距离减少到有界差分矩阵的最大+积，可以在真正的次立方时间内解决[Bringmann等人，Proceedings of the IEEE第57届计算机科学基础年度研讨会，2016,pp. 375-384]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.