A characterization of the tree T∗ such that BP(T∗) = ↔ 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.

Balanced parenthesis representation, Data structures, Isomorphisms, Succinct tree representation
dx.doi.org/10.4230/LIPIcs.CPM.2018.18
Leibniz International Proceedings in Informatics
Annual Symposium on Combinatorial Pattern Matching
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Chikhi, R, & Schönhuth, A. (2018). Dualities in tree representations. In 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018. doi:10.4230/LIPIcs.CPM.2018.18