Communication Dans Un Congrès Année : 2022

An Improved Algorithm for The k-Dyck Edit Distance Problem

Résumé

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 + k^16) time. In this work, we design new algorithms for the threshold Dyck edit distance problem which costs O(n + k^4.544184) time with high probability or O(n + k^4.853059) 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.
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Dates et versions

hal-03943034 , version 1 (17-01-2023)

Identifiants

  • HAL Id : hal-03943034 , version 1

Citer

Dvir Fried, Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, Ely Porat, et al.. An Improved Algorithm for The k-Dyck Edit Distance Problem. 33rd SODA 2022, 2022, Alexandria ( Virtual Conference), United States. ⟨hal-03943034⟩
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