Fine-Grained Complexity of Regular Expression Pattern Matching and Membership
Abstract
The currently fastest algorithm for regular expression pattern matching and membership improves the classical O(nm) time algorithm by a factor of about log^{3/2}n. Instead of focussing on general patterns we analyse homogeneous patterns of bounded depth in this work. For them a classification splitting the types in easy (strongly sub-quadratic) and hard (essentially quadratic time under SETH) is known. We take a very fine-grained look at the hard pattern types from this classification and show a dichotomy: few types allow super-poly-logarithmic improvements while the algorithms for the other pattern types can only be improved by a constant number of log-factors, assuming the Formula-SAT Hypothesis.
Cite
@article{arxiv.2008.02769,
title = {Fine-Grained Complexity of Regular Expression Pattern Matching and Membership},
author = {Philipp Schepper},
journal= {arXiv preprint arXiv:2008.02769},
year = {2020}
}
Comments
Full version of the paper accepted at ESA 2020; v2: typos and reference to conference version corrected