On the Hardness of Computing the Edit Distance of Shallow Trees

Panagiotis Charalampopoulos; Paweł Gawrychowski; Shay Mozes; Oren Weimann

doi:10.1007/978-3-031-20643-6_21

On the Hardness of Computing the Edit Distance of Shallow Trees

Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, Oren Weimann

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
Title of host publication	String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings
Editors	Diego Arroyuelo, Diego Arroyuelo, Barbara Poblete
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	290-302
Number of pages	13
ISBN (Print)	9783031206429
DOIs	https://doi.org/10.1007/978-3-031-20643-6_21
State	Published - 2022
Event	29th International Symposium on String Processing and Information Retrieval, SPIRE 2022 - Concepción, Chile Duration: 8 Nov 2022 → 10 Nov 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13617 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	29th International Symposium on String Processing and Information Retrieval, SPIRE 2022
Country/Territory	Chile
City	Concepción
Period	8/11/22 → 10/11/22

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

Access to Document

10.1007/978-3-031-20643-6_21

Cite this

Charalampopoulos, P., Gawrychowski, P., Mozes, S., & Weimann, O. (2022). On the Hardness of Computing the Edit Distance of Shallow Trees. In D. Arroyuelo, D. Arroyuelo, & B. Poblete (Eds.), String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings (pp. 290-302). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13617 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20643-6_21

Charalampopoulos, Panagiotis ; Gawrychowski, Paweł ; Mozes, Shay et al. / On the Hardness of Computing the Edit Distance of Shallow Trees. String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings. editor / Diego Arroyuelo ; Diego Arroyuelo ; Barbara Poblete. Springer Science and Business Media Deutschland GmbH, 2022. pp. 290-302 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We consider the edit distance problem on rooted ordered trees parameterized by the trees{\textquoteright} 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} ).",

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Charalampopoulos, P, Gawrychowski, P, Mozes, S & Weimann, O 2022, On the Hardness of Computing the Edit Distance of Shallow Trees. in D Arroyuelo, D Arroyuelo & B Poblete (eds), String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13617 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 290-302, 29th International Symposium on String Processing and Information Retrieval, SPIRE 2022, Concepción, Chile, 8/11/22. https://doi.org/10.1007/978-3-031-20643-6_21

On the Hardness of Computing the Edit Distance of Shallow Trees. / Charalampopoulos, Panagiotis; Gawrychowski, Paweł; Mozes, Shay et al.
String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings. ed. / Diego Arroyuelo; Diego Arroyuelo; Barbara Poblete. Springer Science and Business Media Deutschland GmbH, 2022. p. 290-302 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13617 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Charalampopoulos P, Gawrychowski P, Mozes S, Weimann O. On the Hardness of Computing the Edit Distance of Shallow Trees. In Arroyuelo D, Arroyuelo D, Poblete B, editors, String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 290-302. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-20643-6_21