Position Heaps for Parameterized Strings

TL;DR

This paper introduces the parameterized position heap, an efficient indexing structure for parameterized strings, enabling linear-time pattern matching and occurrence retrieval, which advances string indexing techniques for complex pattern matching scenarios.

Contribution

The paper presents the first online linear-time construction algorithm for parameterized position heaps, facilitating efficient pattern matching in parameterized strings.

Findings

Linear-time construction algorithm for parameterized position heap

Efficient linear-time pattern matching in parameterized strings

Applicable to large texts and complex pattern matching scenarios

Abstract

We propose a new indexing structure for parameterized strings, called parameterized position heap. Parameterized position heap is applicable for parameterized pattern matching problem, where the pattern matches a substring of the text if there exists a bijective mapping from the symbols of the pattern to the symbols of the substring. We propose an online construction algorithm of parameterized position heap of a text and show that our algorithm runs in linear time with respect to the text size. We also show that by using parameterized position heap, we can find all occurrences of a pattern in the text in linear time with respect to the product of the pattern size and the alphabet size.