Related papers: A Two Query Adaptive Bitprobe Scheme Storing Five …
One of the central problems in the design of compressed data structures is the efficient support for rank and select queries on bitvectors. These two operations form the backbone of more complex data structures (such as wavelet trees) used…
Due to the increasing demand for cloud services and the threat of privacy invasion, the user is suggested to encrypt the data before it is outsourced to the remote server. The safe storage and efficient retrieval of d-dimensional data on an…
This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…
Suppose there is a large file which should be transmitted (or stored) and there are several (say, m) admissible data-compressors. It seems natural to try all the compressors and then choose the best, i.e. the one that gives the shortest…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
In statistical learning, a dataset is often partitioned into two parts: the training set and the holdout (i.e., testing) set. For instance, the training set is used to learn a predictor, and then the holdout set is used for estimating the…
The Huge Object model for distribution testing, first defined by Goldreich and Ron in 2022, combines the features of classical string testing and distribution testing. In this model we are given access to independent samples from an unknown…
Motivation: Second generation sequencing technology makes it feasible for many researches to obtain enough sequence reads to attempt the de novo assembly of higher eukaryotes (including mammals). De novo assembly not only provides a tool…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms…
Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
In many applications of clustering (for example, ontologies or clusterings of animal or plant species), hierarchical clusterings are more descriptive than a flat clustering. A hierarchical clustering over $n$ elements is represented by a…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely…
We show how to answer spatial multiple-set intersection queries in O(n(log w)/w + kt) expected time, where n is the total size of the t sets involved in the query, w is the number of bits in a memory word, k is the output size, and c is any…
Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…