On the Hardness of Computing the Edit Distance of Shallow Trees

Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, Oren Weimann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the edit distance problem on rooted ordered trees parameterized by the trees’ depth. For two trees of size at most n and depth at most d, the state-of-the-art solutions of Zhang and Shasha [SICOMP 1989] and Demaine et al. [TALG 2009] have runtimes O(n2d2) and O(n3), respectively, and are based on so-called decomposition algorithms. It has been recently shown by Bringmann et al. [TALG 2020] that, when d= Θ(n), one cannot compute the edit distance of two trees in O(n3-ϵ) time (for any constant ϵ> 0 ) under the APSP hypothesis. However, for small values of d, it is not known whether the O(n2d2) upper bound of Zhang and Shasha is optimal. We make the following twofold contribution. First, we show that under the APSP hypothesis there is no algorithm with runtime O(n2d1-ϵ) (for any constant ϵ> 0 ) when d= p oly(n). Second, we show that there is no decomposition algorithm that runs in time o(min { n2d2, n3} ).

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings
EditorsDiego Arroyuelo, Diego Arroyuelo, Barbara Poblete
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783031206429
StatePublished - 2022
Event29th International Symposium on String Processing and Information Retrieval, SPIRE 2022 - Concepción, Chile
Duration: 8 Nov 202210 Nov 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13617 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th International Symposium on String Processing and Information Retrieval, SPIRE 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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