On-line construction of position heaps

TL;DR

This paper introduces a simple, linear-time online algorithm for constructing position heaps of strings, differing slightly from previous definitions, and enabling efficient string matching through an augmented structure.

Contribution

It presents a new on-line construction algorithm for position heaps that is simpler and based on suffix pointers, extending previous work with a novel approach.

Findings

Linear-time construction algorithm for position heaps

Extension to augmented position heaps for efficient string matching

Difference in definition considering suffixes from left to right

Abstract

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it considers the suffixes ordered from left to right. Our construction is based on classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees [Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into the augmented position heap that allows for a linear-time string matching algorithm [Ehrenfeucht et al, 2011].