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 $O(\vert \vert P \vert \vert + n^2)$ time and $O(\vert \vert P \vert \vert +n\times \min (n,\max \{|s|:s\in P\}))$ space, where $\vert \vert P \vert \vert$ is the sum of lengths of the n strings in P. We present a new algorithm of $O(\vert \vert P \vert \vert \log n)$ time and $O(\vert \vert P \vert \vert )$ space to compute the HOG, which exploits the segment tree data structure. We also propose an alternative algorithm using $O(\vert \vert P \vert \vert \frac{\log n}{\log \log n})$ time and $O(\vert \vert P \vert \vert )$ space in the word RAM model of computation.

S. G. Park and K. Park—Supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems).

E. Rivals—ER thanks funding Labex NUMEV, GEM project (ANR 2011-LABX-076).