Improved Range Minimum Queries

Héctor Ferrada and Gonzalo Navarro

Fischer and Heun [SICOMP 2011] proposed the first Range Minimum Query (RMQ) data structure on an array A[1,n] that uses 2n+o(n) bits and answers queries in O(1) time without accessing A. Their scheme converts the Cartesian tree of A into a general tree, which is represented using DFUDS. We show that, by using instead the BP representation, the formula becomes simpler since border conditions are eliminated. We also improve the current implementation of the BP representation for this purpose. This leads to the fastest and most compact practical implementation to date.