A Faster CREW PRAM Algorithm for Computing Cartesian Trees

Cartesian tree is a fundamental data structure with many applications in the areas of data structures and string processing. In this paper, we study the construction of a Cartesian tree on a parallel computation model. We present a CREW PRAM algorithm that runs in O(logn) parallel time and has linear work and space. This improves upon the best previous result of Blelloch and Shun which takes O(log2 n) time and linear work/space.