Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Fusion trees can be implemented with AC0 instructions only
Theoretical Computer Science
Multidimensional divide-and-conquer
Communications of the ACM
Optimal Algorithms for List Indexing and Subset Rank
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
New Upper Bounds for Generalized Intersection Searching Problems
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Frequency Estimation of Internet Packet Streams with Limited Space
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A simple algorithm for finding frequent elements in streams and bags
ACM Transactions on Database Systems (TODS)
New Lower Bound Techniques for Dynamic Partial Sums and Related Problems
SIAM Journal on Computing
Optimal External Memory Interval Management
SIAM Journal on Computing
Approximate colored range and point enclosure queries
Journal of Discrete Algorithms
Beyond simple aggregates: indexing for summary queries
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Counting colours in compressed strings
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
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
Linear-Space data structures for range minority query in arrays
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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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Given a set P of n coloured points on the real line, we study the problem of answering range α-majority (or "heavy hitter") queries on P. More specifically, for a query range Q, we want to return each colour that is assigned to more than an α-fraction of the points contained in Q. We present a new data structure for answering range α-majority queries on a dynamic set of points, where α∈(0,1). Our data structure uses O(n) space, supports queries in $O((\lg n) / \alpha)$ time, and updates in $O((\lg n) / \alpha)$ amortized time. If the coordinates of the points are integers, then the query time can be improved to $O(\lg n / (\alpha \lg \lg n))$. For constant values of α, this improved query time matches an existing lower bound, for any data structure with polylogarithmic update time. We also generalize our data structure to handle sets of points in d-dimensions, for d≥2, as well as dynamic arrays, in which each entry is a colour.