TY - GEN

T1 - An Improved Algorithm for The k-Dyck Edit Distance Problem

AU - Fried, Dvir

AU - Golan, Shay

AU - Kociumaka, Tomasz

AU - Kopelowitz, Tsvi

AU - Porat, Ely

AU - Starikovskaya, Tatiana

N1 - Publisher Copyright: Copyright © 2022 by SIAM.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85121626282&partnerID=8YFLogxK

M3 - منشور من مؤتمر

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 3650

EP - 3669

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2022

T2 - 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022

Y2 - 9 January 2022 through 12 January 2022

ER -