An overview of data warehousing and OLAP technology
ACM SIGMOD Record
A unifying look at data structures
Communications of the ACM
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching
SIAM Journal on Computing
Representing Trees of Higher Degree
Algorithmica
Compressed Suffix Trees with Full Functionality
Theory of Computing Systems
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
A Uniform Approach Towards Succinct Representation of Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
On Cartesian Trees and Range Minimum Queries
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Data structures for range minimum queries in multidimensional arrays
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On space efficient two dimensional range minimum data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Space-Efficient Preprocessing Schemes for Range Minimum Queries on Static Arrays
SIAM Journal on Computing
Encoding 2d range maximum queries
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Two-dimensional range minimum queries
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Encoding 2d range maximum queries
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Succinct indices for range queries with applications to orthogonal range maxima
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Two dimensional range minimum queries and fibonacci lattices
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider the two-dimensional range maximum query (2D-RMQ) problem: given an array A of ordered values, to pre-process it so that we can find the position of the largest element in a (user-specified) range of rows and range of columns. We focus on determining the effective entropy of 2D-RMQ, i.e., how many bits are needed to encode A so that 2D-RMQ queries can be answered without access to A. We give tight upper and lower bounds on the expected effective entropy for the case when A contains independent identically-distributed random values, and new upper and lower bounds for arbitrary A, for the case when A contains few rows. The latter results improve upon upper and lower bounds by Brodal et al. (ESA 2010). We also give some efficient data structures for 2D-RMQ whose space usage is close to the effective entropy.