A Linear Time Algorithm for Constructing Hierarchical Overlap Graphs

TL;DR

This paper introduces a new linear time algorithm for constructing hierarchical overlap graphs (HOG), significantly improving efficiency over previous methods by reducing time and space complexity to linear scale.

Contribution

The paper presents the first linear time and space algorithm for constructing hierarchical overlap graphs, outperforming existing methods.

Findings

HOG construction achieved in O(||P||) time and space

Improved over previous O(||P|| log n) algorithms

Reduces complexity compared to overlap graph construction

Abstract

The hierarchical overlap graph (HOG) is a graph that encodes overlaps from a given set P of n strings, as the overlap graph does. A best known algorithm constructs HOG in O(||P|| log n) time and O(||P||) space, where ||P|| is the sum of lengths of the strings in P. In this paper we present a new algorithm to construct HOG in O(||P||) time and space. Hence, the construction time and space of HOG are better than those of the overlap graph, which are O(||P|| + n^2).