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STACS
2012
Springer

Linear-Space Data Structures for Range Mode Query in Arrays

8 years 5 months ago
Linear-Space Data Structures for Range Mode Query in Arrays
A mode of a multiset S is an element a ∈ S of maximum multiplicity; that is, a occurs at least as frequently as any other element in S. Given an array A[1 : n] of n elements, we consider a basic problem: constructing a static data structure that efficiently answers range mode queries on A. Each query consists of an input pair of indices (i, j) for which a mode of A[i : j] must be returned. The best previous data structure with linear space, by Krizanc, Morin, and Smid (ISAAC 2003), requires O( √ n log log n) query time. We improve their result and present an O(n)-space data structure that supports range mode queries in O( p n/ log n) worst-case time. Furthermore, we present strong evidence that a query time significantly below √ n cannot be achieved by purely combinatorial techniques; we show that boolean matrix multiplication of two √ n × √ n matrices reduces to n range mode queries in an array of size O(n). Additionally, we give linear-space data structures for orthogona...
Timothy M. Chan, Stephane Durocher, Kasper Green L
Added 25 Apr 2012
Updated 25 Apr 2012
Type Journal
Year 2012
Where STACS
Authors Timothy M. Chan, Stephane Durocher, Kasper Green Larsen, Jason Morrison, Bryan T. Wilkinson
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