Inferring Strings from Position Heaps in Linear Time

TL;DR

This paper presents linear-time algorithms for reconstructing text strings from position heaps, including variants where labels or node numbers are missing, advancing string indexing methods.

Contribution

It introduces efficient algorithms for inverse position heap problems, enabling string reconstruction from incomplete or partially labeled trees.

Findings

Linear-time algorithms for string reconstruction

Handling missing labels and node numbers

Improved methods for position heap inversion

Abstract

Position heaps are index structures of text strings used for the string matching problem. They are rooted trees whose edges and nodes are labeled and numbered, respectively. This paper is concerned with variants of the inverse problem of position heap construction and gives linear-time algorithms for those problems. The basic problem is to restore a text string from a rooted tree with labeled edges and numbered nodes. In the variant problems, the input trees may miss edge labels or node numbers which we must restore as well.