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Communication Dans Un Congrès Année : 2012

Linear-Space Data Structures for Range Mode Query in Arrays

Timothy M. Chan
  • Fonction : Auteur
Stephane Durocher
  • Fonction : Auteur
Kasper Green Larsen
  • Fonction : Auteur
Jason Morrison
  • Fonction : Auteur
Bryan T. Wilkinson
  • Fonction : Auteur

Résumé

A mode of a multiset S is an element a in 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(sqrt(n) loglog n) query time. We improve their result and present an O(n)-space data structure that supports range mode queries in O(sqrt(n / log n)) worst-case time. Furthermore, we present strong evidence that a query time significantly below sqrt(n) cannot be achieved by purely combinatorial techniques; we show that boolean matrix multiplication of two sqrt(n) by sqrt(n) matrices reduces to n range mode queries in an array of size O(n). Additionally, we give linear-space data structures for orthogonal range mode in higher dimensions (queries in near O(n^(1-1/2d)) time) and for halfspace range mode in higher dimensions (queries in O(n^(1-1/d^2)) time).
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hal-00678196 , version 1 (03-02-2012)

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  • HAL Id : hal-00678196 , version 1

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Timothy M. Chan, Stephane Durocher, Kasper Green Larsen, Jason Morrison, Bryan T. Wilkinson. Linear-Space Data Structures for Range Mode Query in Arrays. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.290-301. ⟨hal-00678196⟩

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