On Cartesian Trees and Range Minimum Queries

Authors:
Erik D. Demaine;Gad M. Landau;Oren Weimann
Affiliations:
MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA;Department of Computer Science, University of Haifa, Haifa, Israeal and Department of Computer and Information Science, Polytechnic Institute of NYU,;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA
Venue:
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Year:
2009

Citing 24
Cited 7

Fast algorithms for finding nearest common ancestors

SIAM Journal on Computing
The input/output complexity of sorting and related problems

Communications of the ACM
On finding lowest common ancestors: simplification and parallelization

SIAM Journal on Computing
Computing partial sums in multidimensional arrays

SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Recursive star-tree parallel data structure

SIAM Journal on Computing
A randomized linear-time algorithm to find minimum spanning trees

Journal of the ACM (JACM)
Optimal on-line decremental connectivity in trees

Information Processing Letters
An On-Line Edge-Deletion Problem

Journal of the ACM (JACM)
A minimum spanning tree algorithm with inverse-Ackermann type complexity

Journal of the ACM (JACM)
An optimal minimum spanning tree algorithm

Journal of the ACM (JACM)
Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An Inverse-Ackermann Style Lower Bound for the Online Minimum Spanning Tree

FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Cache-oblivious data structures for orthogonal range searching

Proceedings of the nineteenth annual symposium on Computational geometry
Cache-Oblivious Algorithms

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems

STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Cache-oblivious string dictionaries

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees--History of Combinatorial Generation (Art of Computer Programming)

The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees--History of Combinatorial Generation (Art of Computer Programming)
All-pairs bottleneck paths for general graphs in truly sub-cubic time

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
All-pairs bottleneck paths in vertex weighted graphs

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Cache-Oblivious Priority Queue and Its Application to Graph Algorithms

SIAM Journal on Computing
Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Lowest common ancestors in trees and directed acyclic graphs

Journal of Algorithms
Theoretical and practical improvements on the RMQ-Problem, with applications to LCA and LCE

CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Two-dimensional range minimum queries

CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching

Data structures for range minimum queries in multidimensional arrays

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Path minima queries in dynamic weighted trees

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Range selection and median: tight cell probe lower bounds and adaptive data structures

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Encoding 2d range maximum queries

ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Characterizing (quasi-)ultrametric finite spaces in terms of (directed) graphs

Discrete Applied Mathematics
Linear-Space data structures for range minority query in arrays

SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Two dimensional range minimum queries and fibonacci lattices

ESA'12 Proceedings of the 20th Annual European conference on Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.