Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
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
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
A unifying look at data structures
Communications of the ACM
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals
Data Mining and Knowledge Discovery
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Optimal Range Max Datacube for Fixed Dimensions
ICDT '03 Proceedings of the 9th International Conference on Database Theory
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Generatingfunctionology
Linear Verification For Spanning Trees
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
On Cartesian Trees and Range Minimum Queries
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Two-dimensional range minimum queries
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
On space efficient two dimensional range minimum data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Computing toolpaths for 5-axis NC machines
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Space-Efficient Preprocessing Schemes for Range Minimum Queries on Static Arrays
SIAM Journal on Computing
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
Minimizing average interference through topology control
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Range aggregate maximal points in the plane
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Encoding 2d range maximum queries
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Computing feasible toolpaths for 5-axis machines
Theoretical Computer Science
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
I/O-efficient planar range skyline and attrition priority queues
Proceedings of the 32nd symposium on Principles of database systems
Faster algorithm to find anti-risk path between two nodes of an undirected graph
Journal of Combinatorial Optimization
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Given a d-dimensional array A with N entries, the Range Minimum Query (RMQ) asks for the minimum element within a contiguous subarray of A. The 1D RMQ problem has been studied intensively because of its relevance to the Nearest Common Ancestor problem and its important use in stringology. If constant-time query answering is required, linear time and space preprocessing algorithms were known for the 1D case, but not for the higher dimensional cases. In this paper, we give the first linear-time preprocessing algorithm for arrays with fixed dimension, such that any range minimum query can be answered in constant time.