
TL;DR
This paper introduces efficient algorithms for detecting 3-cadences in binary strings, both compressed and uncompressed, and proves NP-completeness for certain variants of the problem in grammar-compressed strings.
Contribution
It provides the first polynomial-time detection algorithm for 3-cadences in grammar-compressed binary strings and establishes NP-completeness results for related problems.
Findings
Polynomial-time algorithm for 3-cadence detection in grammar-compressed binary strings
Linear-time detection algorithm for uncompressed binary strings
NP-completeness of several cadence detection variants in grammar-compressed strings
Abstract
Cadences are structurally maximal arithmetic progressions of indices corresponding to equal characters in an underlying string. This paper provides a polynomial time detection algorithm for 3-cadences in grammar-compressed binary strings. This algorithm also translates to a linear time detection algorithm for 3-cadences in uncompressed binary strings. Furthermore, this paper proves that several variants of the cadence detection problem are NP-complete for grammar-compressed strings. As a consequence, the equidistant subsequence matching problem with patterns of length three is NP-complete for grammar-compressed ternary strings.
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