The Heaviest Induced Ancestors Problem Revisited

Abedin, Paniz; Hooshmand, Sahar; Ganguly, Arnab; Thankachan, Sharma V.

doi:10.4230/lipics.cpm.2018.20

Cited by 5 publications

(4 citation statements)

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“…However, in their solution, after each edit operation, the string is immediately reverted to its original version. Abedin et al [1] improved the tradeoffs for this problem by designing a more efficient solution for the so-called heaviest induced ancestors problem. Amir and Boneh [3] investigated some special cases of the partially dynamic LCS problem (in which one of the strings is assumed to be static); namely, the case where the static string is periodic and the case where the substitutions in the dynamic string are substitutions with some letter # ∈ Σ.…”

Section: Problem: Longest Common Substringmentioning

confidence: 99%

“…We reduce this problem to answering a heaviest induced ancestors (HIA) query. This reduction was also presented in [1,6], but we describe the details to make following the more involved solution of fully dynamic LCS easier.…”

Section: Problem: Longest Common Substringmentioning

confidence: 99%

“…We try to anchor the LCS in both strings as follows. For each of the strings S and T we show how to maintain, in log O (1) n time, a collection of pairs of adjacent fragments (e.g. (S[i .…”

Section: Problem: Longest Common Substringmentioning

confidence: 99%

“…Then, the problem in scope can be restated as follows: given two fragments U and V of T compute the longest fragment of U V that occurs in T . This problem can be reduced to a single HIA query over the suffix trees of T and T R as shown in [1,6] and we provide a brief overview at the end of this section. Combining the above discussion with Lemmas 2.2 and 3.4 we obtain that an LCS can be maintained after an O(n log 2 n) time preprocessing in O(log 2 n) time per update.…”

Section: Partially Dynamic Lcsmentioning

confidence: 99%

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Dynamic Longest Common Substring in Polylogarithmic Time

Charalampopoulos,

Gawrychowski,

Pokorski

2020

Preprint

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The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings S and T , each of length at most n, that undergo substitutions of letters, in order to be able to return a longest common substring after each substitution. Recently, Amir et al. [ESA 2019] presented a solution for this problem that needs only Õ(n 2/3 ) time per update. This brought the challenge of determining whether there exists a faster solution with polylogarithmic update time, or (as is the case for other dynamic problems), we should expect a polynomial (conditional) lower bound. We answer this question by designing a significantly faster algorithm that processes each substitution in amortized log O(1) n time with high probability. Our solution relies on exploiting the local consistency of the parsing of a collection of dynamic strings due to Gawrychowski et al. [SODA 2018], and on maintaining two dynamic trees with labeled bicolored leaves, so that after each update we can report a pair of nodes, one from each tree, of maximum combined weight, which have at least one common leaf-descendant of each color. We complement this with a lower bound of Ω(log n/ log log n) for the update time of any polynomial-size data structure that maintains the LCS of two dynamic strings, and the same lower bound for the update time of any data structure of size Õ(n) that maintains the LCS of a static and a dynamic string. Both lower bounds hold even allowing amortization and randomization.

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Section: Problem: Longest Common Substringmentioning

confidence: 99%

Section: Problem: Longest Common Substringmentioning

confidence: 99%

“…We try to anchor the LCS in both strings as follows. For each of the strings S and T we show how to maintain, in log O (1) n time, a collection of pairs of adjacent fragments (e.g. (S[i .…”

Section: Problem: Longest Common Substringmentioning

confidence: 99%

Section: Partially Dynamic Lcsmentioning

confidence: 99%

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