English

Detecting One-variable Patterns

Data Structures and Algorithms 2017-07-19 v5

Abstract

Given a pattern p=s1x1s2x2sr1xr1srp = s_1x_1s_2x_2\cdots s_{r-1}x_{r-1}s_r such that x1,x2,,xr1{x,x}x_1,x_2,\ldots,x_{r-1}\in\{x,\overset{{}_{\leftarrow}}{x}\}, where xx is a variable and x\overset{{}_{\leftarrow}}{x} its reversal, and s1,s2,,srs_1,s_2,\ldots,s_r are strings that contain no variables, we describe an algorithm that constructs in O(rn)O(rn) time a compact representation of all PP instances of pp in an input string of length nn over a polynomially bounded integer alphabet, so that one can report those instances in O(P)O(P) time.

Keywords

Cite

@article{arxiv.1604.00054,
  title  = {Detecting One-variable Patterns},
  author = {Dmitry Kosolobov and Florin Manea and Dirk Nowotka},
  journal= {arXiv preprint arXiv:1604.00054},
  year   = {2017}
}

Comments

16 pages (+13 pages of Appendix), 4 figures, accepted to SPIRE 2017

R2 v1 2026-06-22T13:22:49.648Z