Efficient Pattern Matching in Elastic-Degenerate Strings

TL;DR

This paper introduces an efficient algorithm for pattern matching in elastic-degenerate strings, extending gapped strings to handle variable-length sets of substrings, with practical efficiency due to small constants.

Contribution

It presents the first algorithm for pattern matching in elastic-degenerate strings with a detailed time complexity analysis and linear space usage for certain cases.

Findings

Algorithm runs in O(N+αγnm) time, efficient for small constants.

Linear space complexity for a constant number of elastic-degenerate symbols.

Expected practical efficiency due to small constants in real applications.

Abstract

In this paper, we extend the notion of gapped strings to elastic-degenerate strings. An elastic-degenerate string can been seen as an ordered collection of k > 1 seeds (substrings/subpatterns) interleaved by elastic-degenerate symbols such that each elastic-degenerate symbol corresponds to a set of two or more variable length strings. Here, we present an algorithm for solving the pattern matching problem with (solid) pattern and elastic-degenerate text, running in O(N+{\alpha}{\gamma}nm) time; where m is the length of the given pattern; n and N are the length and total size of the given elastic-degenerate text, respectively; {\alpha} and {\gamma} are small constants, respectively representing the maximum number of strings in any elastic-degenerate symbol of the text and the largest number of elastic-degenerate symbols spanned by any occurrence of the pattern in the text. The space used by the algorithm is linear in the size of the input for a constant number of elastic-degenerate symbols in the text; {\alpha} and {\gamma} are so small in real applications that the algorithm is expected to work very efficiently in practice.