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Dualities in Tree Representations

Authors Rayan Chikhi, Alexander Schönhuth

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Rayan Chikhi
  • CNRS, Université de Lille, CRIStAL, Lille, France
Alexander Schönhuth
  • Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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Rayan Chikhi and Alexander Schönhuth. Dualities in Tree Representations. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 18:1-18:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


A characterization of the tree T^* such that BP(T^*)=ova{DFUDS(T)}, the reversal of DFUDS(T) is given. An immediate consequence is a rigorous characterization of the tree T^ such that BP(T^)=DFUDS(T). In summary, BP and DFUDS are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in BP and/or DFUDS. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent work on the Range Minimum Query problem, and to provide improvements for the Minimum Length Interval Query problem.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Trees
  • Data Structures
  • Succinct Tree Representation
  • Balanced Parenthesis Representation
  • Isomorphisms


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