An Improved Algorithm for The k-Dyck Edit Distance Problem

Dvir Fried; Shay Golan; Tomasz Kociumaka; Tsvi Kopelowitz; Ely Porat; Tatiana Starikovskaya

An Improved Algorithm for The k-Dyck Edit Distance Problem

Dvir Fried, Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, Ely Porat, Tatiana Starikovskaya

Department of Computer Science

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

8 Scopus citations

Abstract

A Dyck sequence is a sequence of opening and closing parentheses (of various types) that is balanced. The Dyck edit distance of a given sequence of parentheses S is the smallest number of edit operations (insertions, deletions, and substitutions) needed to transform S into a Dyck sequence. We consider the threshold Dyck edit distance problem, where the input is a sequence of parentheses S and a positive integer k, and the goal is to compute the Dyck edit distance of S only if the distance is at most k, and otherwise report that the distance is larger than k. Backurs and Onak [PODS'16] showed that the threshold Dyck edit distance problem can be solved in O(n + k16) time. In this work, we design new algorithms for the threshold Dyck edit distance problem which costs O(n + k4.782036) time with high probability or O(n + k4.853059) ) deterministically. Our algorithms combine several new structural properties of the Dyck edit distance problem, a refined algorithm for fast (min, +) matrix product, and a careful modification of ideas used in Valiant's parsing algorithm.

Original language	English
Title of host publication	ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Publisher	Association for Computing Machinery
Pages	3650-3669
Number of pages	20
ISBN (Electronic)	9781611977073
State	Published - 2022
Event	33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States Duration: 9 Jan 2022 → 12 Jan 2022

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	2022-January

Conference

Conference	33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Country/Territory	United States
City	Alexander
Period	9/01/22 → 12/01/22

Bibliographical note

Publisher Copyright:
Copyright © 2022 by SIAM.

Funding

∗Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel. Supported in part by ISF grants no. 1278/16 and 1926/19, by a BSF grant no. 2018364, and by an ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064). †University of California, Berkeley, USA. Partly supported by Fulbright Postdoctoral Fellowship. ‡University of California, Berkeley, USA. Partly supported by NSF 1652303, 1909046, and HDR TRIPODS 1934846 grants, and an Alfred P. Sloan Fellowship. §DI/ENS, PSL Research University, France. Partially supported by the grant ANR-20-CE48-0001 from the French National Research Agency (ANR).

Funders	Funder number
Alfred P. Sloan Fellowship	ANR-20-CE48-0001
National Science Foundation	1909046, 1652303, 1934846
European Commission
Agence Nationale de la Recherche
United States-Israel Binational Science Foundation	2018364
Israel Science Foundation	1926/19, 1278/16
Horizon 2020	683064

Cite this

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title = "An Improved Algorithm for The k-Dyck Edit Distance Problem",

abstract = "A Dyck sequence is a sequence of opening and closing parentheses (of various types) that is balanced. The Dyck edit distance of a given sequence of parentheses S is the smallest number of edit operations (insertions, deletions, and substitutions) needed to transform S into a Dyck sequence. We consider the threshold Dyck edit distance problem, where the input is a sequence of parentheses S and a positive integer k, and the goal is to compute the Dyck edit distance of S only if the distance is at most k, and otherwise report that the distance is larger than k. Backurs and Onak [PODS'16] showed that the threshold Dyck edit distance problem can be solved in O(n + k16) time. In this work, we design new algorithms for the threshold Dyck edit distance problem which costs O(n + k4.782036) time with high probability or O(n + k4.853059) ) deterministically. Our algorithms combine several new structural properties of the Dyck edit distance problem, a refined algorithm for fast (min, +) matrix product, and a careful modification of ideas used in Valiant's parsing algorithm.",

author = "Dvir Fried and Shay Golan and Tomasz Kociumaka and Tsvi Kopelowitz and Ely Porat and Tatiana Starikovskaya",

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Fried, D, Golan, S, Kociumaka, T, Kopelowitz, T , Porat, E & Starikovskaya, T 2022, An Improved Algorithm for The k-Dyck Edit Distance Problem. in ACM-SIAM Symposium on Discrete Algorithms, SODA 2022. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2022-January, Association for Computing Machinery, pp. 3650-3669, 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, Alexander, United States, 9/01/22.

An Improved Algorithm for The k-Dyck Edit Distance Problem. / Fried, Dvir; Golan, Shay; Kociumaka, Tomasz et al.
ACM-SIAM Symposium on Discrete Algorithms, SODA 2022. Association for Computing Machinery, 2022. p. 3650-3669 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2022-January).

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

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An Improved Algorithm for The k-Dyck Edit Distance Problem

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