Asymptotically Optimal Encodings of Range Data Structures for Selection and Top-k Queries

Given an array A[1, n] of elements with a total order, we consider the problem of building a data structure that solves two queries: (a) selection queries receive a range [i, j] and an integer k and return the position of the kth largest element in A[i, j]; (b) top-k queries receive [i, j] and k and return the positions of the k largest elements in A[i, j]. These problems can be solved in optimal time, O(1 + lg k/ lg lg n) and O(k), respectively, using linear-space data structures. We provide the first study of the encoding data structures for the above problems, where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A, and their positions, rather their actual values, and thus we do not need to keep A at query time. In those cases, encodings save storage space: we first show that any encoding answering such queries requires n lg k − O(n + k lg k) bits of space; then, we design encodings using O(n lg k) bits, that is, asymptotically optimal up to constant factors, while preserving optimal query time.Peer-reviewedPost-prin

Additional file 4: of Statistical modeling for sensitive detection of low-frequency single nucleotide variants

Genomic sequence context features used in GLM. (PDF 71 kb

Additional file 5: of Statistical modeling for sensitive detection of low-frequency single nucleotide variants

Vuong’s non-nested test on 4 distributions applied to Illumina MiSeq training data. (PDF 65 kb

Additional file 10: of Statistical modeling for sensitive detection of low-frequency single nucleotide variants

Zero-inflated Negative Binomial GLM coefficients for Illumina MiSeq training datasets. (PDF 70 kb

Additional file 6: of Dependence receptor UNC5A restricts luminal to basal breast cancer plasticity and metastasis

Summary of results of RNA-seq of sh-Control and sh5-UNC5A clones of MCF7 and T-47D cells. Various comparisons are shown. (XLSX 859 kb

Additional file 5: of Dependence receptor UNC5A restricts luminal to basal breast cancer plasticity and metastasis

The effect of ICI-182,780 (Fulvestrant) treatment on UNC5A knockdown cells and Western blot showing UNC5A knockdown by CRISPR in MCF-7 cells. (PSD 3346 kb