Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Range mode and range median queries on lists and trees
Nordic Journal of Computing
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Approximate range mode and range median queries
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Range mode and range median queries in constant time and sub-quadratic space
Information Processing Letters
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Range Quantile Queries: Another Virtue of Wavelet Trees
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Cell probe lower bounds and approximations for range mode
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Theoretical Computer Science
Range majority in constant time and linear space
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
New algorithms on wavelet trees and applications to information retrieval
Theoretical Computer Science
Path queries in weighted trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Dynamic range selection in linear space
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Linear-Space data structures for range minority query in arrays
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Range majority in constant time and linear space
Information and Computation
Better space bounds for parameterized range majority and minority
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We investigate the following problem: Given a list of n items and a function defined over lists of these items, generate a bounded amount of auxiliary information such that range queries asking for the value of the function on sub-lists can be answered within a certain time bound. For the function "mode" we improve the previously known time bound O(nƐ log n) to O(nƐ) with space O(n2-2Ɛ), where 0 ≤ Ɛ O(n2 log log n/ log n) for an O(1) time bounded solution to O(n2/ log n). For the function "median" the space bound O(n2 log log n/ log n) is improved to O(n2 log(k) n/ log n) for an O(1) time solution, where k is an arbitrary constant and log(k) is the iterated logarithm.