Efficient Construction of Hierarchical Overlap Graphs

Abstract

The hierarchical overlap graph (HOG for short) is an overlap encoding graph that efficiently represents overlaps from a given set P of n strings. A previously known algorithm constructs the HOG in O(||P || + n 2 ) time and O(||P || + n × min(n, max{|s| : s ∈ P })) space, where ||P || is the sum of lengths of the n strings in P . We present a new algorithm of O(||P || log n) time and O(||P ||) space to compute the HOG, which exploits the segment tree data structure. We also propose an alternative algorithm using O(||P || log n log log n ) time and O(||P ||) space in the word RAM model of computation.

Masked superstrings as a unified framework for textualk-mer set representations

“…However, it is not known whether these two algorithms (or indeed any other algorithm) bring any real advantage compared to Greedy. Lastly, we mention a variant of the overlap graph, called the hierarchical overlap graph (HOG) [39], which encodes maximal pairwise overlaps as well, but its size is linear in the input size (compared to quadratic for the overlap graph). Furthermore, linear-time constructions of HOGs have recently been designed [40, 41].…”

A Linear Time Algorithm for Constructing Hierarchical Overlap Graphs

“…For computing the HOG, Cazaux and Rivals proposed an O(||P || + n 2 ) time algorithm using O(||P || + n × min(n, max{|s| : s ∈ P })) space [5]. Recently, Park et al [14] gave an O(||P || log n) time algorithm using O(||P ||) space by using the segment tree data structure.…”