Work

On Strings Having the Same Length-k Substrings

Year: 2026

Type: article

Abstract: Let $$\varvec{\textsf {Substr}}_{\varvec{k}}\varvec{(X)}$$ Substr k ( X ) denote the set of length- $$\varvec{k}$$ k substrings of a given string $$\varvec{X}$$ X for a given integer $$\varvec{k}>\varvec{0}$$ k > 0 . We study the following basic string problem, called $$\varvec{z}$$ z - Shortest $$\varvec{\mathcal {S}}_{\varvec{k}}$$ S k - Equivalent Strings : Given a set $$\varvec{\mathcal {S}}_{\varvec{k}}$$ S k of $$\varvec{n}$$ n length- $$\varvec{k}$$ k strings and an integer $$\varvec{z}>\varvec{0}$$ z > 0 , list $$\varvec{z}$$ z shortest distinct strings $$\varvec{T}_{\varvec{1}}\varvec{,\ldots ,}\varvec{T}_{\varvec{z}}$$ T 1 , … , T z such that $$\varvec{\textsf {Substr}}_{\varvec{k}}\varvec{(}\varvec{T}_{\varvec{i}}\varvec{)}=\varvec{\mathcal {S}}_{\varvec{k}}$$ Substr k ( T

Source: Theory of Computing Systems

DOI: 10.1007/s00224-025-10240-z