TL;DR
This paper introduces a new data structure for the Longest Common Extension problem with wildcards, providing a flexible trade-off between preprocessing time, space, and query efficiency, and establishing its near-optimality under common complexity hypotheses.
Contribution
It presents a simple, parameterized data structure for LCE with wildcards, connecting it to Boolean matrix multiplication and proving near-optimality under standard conjectures.
Findings
Data structure achieves a tunable trade-off between preprocessing, space, and query time.
Connection established between LCE with wildcards and Boolean matrix multiplication.
Applications include efficient algorithms for pattern matching and string analysis with wildcards.
Abstract
We study the Longest Common Extension (LCE) problem in a string containing wildcards. Wildcards (also called "don't cares" or "holes") are special characters that match any other character in the alphabet, similar to the character "?" in Unix commands or "." in regular expression engines. We consider the problem parametrized by , the number of maximal contiguous groups of wildcards in the input string. Our main contribution is a simple data structure for this problem that can be built in time, occupies space, and answers queries in time, for any . Up to the factor, this interpolates smoothly between the data structure of Crochemore et al. [JDA 2015], which has preprocessing time and space, and query time, and a simple solution based on the "kangaroo jumping" technique [Landau and Vishkin, STOC 1986],…
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