Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Journal of the ACM (JACM)
Succinct static data structures
Succinct static data structures
Higher Lower Bounds for Near-Neighbor and Further Rich Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Range mode and range median queries on lists and trees
Nordic Journal of Computing
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Range mode and range median queries in constant time and sub-quadratic space
Information Processing Letters
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
Approximate range mode and range median queries
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Colored range queries and document retrieval
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
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
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
Colored range queries and document retrieval
Theoretical Computer Science
Better space bounds for parameterized range majority and minority
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Spaces, Trees, and Colors: The algorithmic landscape of document retrieval on sequences
ACM Computing Surveys (CSUR)
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The mode of a multiset of labels, is a label that occurs at least as often as any other label. The input to the range mode problem is an array A of size n. A range query [i, j] must return the mode of the subarray A[i], A[i+1],...,A[j]. We prove that any data structure that uses S memory cells of w bits needs Ω(log n/log(Sw/n)) time to answer a range mode query. Secondly, we consider the related range k-frequency problem. The input to this problem is an array A of size n, and a query [i, j] must return whether there exists a label that occurs precisely k times in the subarray A[i], A[i+1],...,A[j]. We show that for any constant k 1, this problem is equivalent to 2D orthogonal rectangle stabbing, and that for k = 1 this is no harder than four-sided 3D orthogonal range emptiness. Finally, we consider approximate range mode queries. A c-approximate range mode query must return a label that occurs at least 1/c times that of the mode. We describe a linear space data structure that supports 3-approximate range mode queries in constant time, and a data structure that uses O(n/ε) space and supports (1 + ε)-approximation queries in O(log 1/ε) time.