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
Recommended Citation
Durocher, S., Shah, R., Skala, M., & Thankachan, S. (2013). Linear-space data structures for range frequency queries on arrays and trees. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8087 LNCS, 325-336. https://doi.org/10.1007/978-3-642-40313-2_30