Filtering search: a new approach to query answering
SIAM Journal on Computing
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Range mode and range median queries on lists and trees
Nordic Journal of Computing
Range mode and range median queries in constant time and sub-quadratic space
Information Processing Letters
On Cartesian Trees and Range Minimum Queries
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
Improved bounds for range mode and range median queries
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Fully-functional succinct trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Finding frequent elements in compressed 2D arrays and strings
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
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
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate range mode and range median queries
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Dynamic range majority data structures
ISAAC'11 Proceedings of the 22nd international conference on Algorithms 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 consider range queries in arrays that search for low-frequency elements: least frequent elements and α-minorities. An α-minority of a query range has multiplicity no greater than an α fraction of the elements in the range. Our data structure for the least frequent element range query problem requires O(n) space, O(n3/2) preprocessing time, and $O(\sqrt{n})$ query time. A reduction from boolean matrix multiplication to this problem shows the hardness of simultaneous improvements in both preprocessing time and query time. Our data structure for the α-minority range query problem requires O(n) space, supports queries in O(1/α) time, and allows α to be specified at query time.