TY - JOUR

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:
© 2024 Copyright held by the owner/author(s).

PY - 2024/6/21

Y1 - 2024/6/21

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+k4.544184) 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+k4.544184) 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.

KW - Dyck language

KW - edit distance

KW - fine-grained complexity

UR - http://www.scopus.com/inward/record.url?scp=85192385565&partnerID=8YFLogxK

U2 - 10.1145/3627539

DO - 10.1145/3627539

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AN - SCOPUS:85192385565

SN - 1549-6325

VL - 20

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 3

ER -