Linear-space data structures for range frequency queries on arrays and trees

Document Type

Conference Proceeding

Publication Date

10-15-2013

Abstract

We present O(n)-space data structures to support various range frequency queries on a given array A[0 : n - 1] or tree T with n nodes. Given a query consisting of an arbitrary pair of pre-order rank indices (i,j), our data structures return a least frequent element, mode, or α-minority of the multiset of elements in the unique path with endpoints at indices i and j in A or T. We describe a data structure that supports range least frequent element queries on arrays in O(√n/w) time, improving the Θ(√n) worst-case time required by the data structure of Chan et al. (SWAT 2012), where w ∈ Ω(log n) is the word size in bits. We describe a data structure that supports range mode queries on trees in O(log log n √n/w) time, improving the Θ(√n log n) worst-case time required by the data structure of Krizanc et al. (ISAAC 2003). Finally, we describe a data structure that supports range α-minority queries on trees in O(α-1 log log n) time, where α ∈ [0,1] is specified at query time. © 2013 Springer-Verlag.

Publication Source (Journal or Book title)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

First Page

325

Last Page

336

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