On Cartesian Trees and Range Minimum Queries

We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree of a tree for the bottleneck edge query problem on trees and undirected graphs, and a proof that no Cartesian tree exists for the two-dimensional version of the range minimum query problem. Key words: Range minimum query, lowest common ancestor, Cartesian tree, cache-oblivious, bottleneck paths, minimum spanning tree verification, partial sums.

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Erik D. Demaine, Gad M. Landau, Oren Weimann
• Keywords: Cartesian Tree Exists, ICALP 2009, Minimum Query Problem, Range Minimum Query, Theoretical Computer Science