A Linear Time Algorithm for Constructing Hierarchical Overlap Graphs

Authors Sangsoo Park , Sung Gwan Park , Bastien Cazaux , Kunsoo Park , Eric Rivals

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Sangsoo Park
  • Samsung Electronics, Seoul, Korea
Sung Gwan Park
  • Samsung Electronics, Seoul, Korea
Bastien Cazaux
  • LIRMM, Université Montpellier, CNRS, Montpellier, France
Kunsoo Park
  • Seoul National University, Seoul, Korea
Eric Rivals
  • LIRMM, Université Montpellier, CNRS, Montpellier, France

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Sangsoo Park, Sung Gwan Park, Bastien Cazaux, Kunsoo Park, and Eric Rivals. A Linear Time Algorithm for Constructing Hierarchical Overlap Graphs. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 22:1-22:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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|| + n²).

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • overlap graph
  • hierarchical overlap graph
  • shortest superstring problem
  • border array


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