Related papers: Optimal Indexes for Sparse Bit Vectors
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
We consider the following problem: Given a set S of at most n elements from a universe of size m, represent it in memory as a bit string so that membership queries of the form "Is x in S?" can be answered by making at most t probes into the…
Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h in H? In the sparse recovery literature, where x is…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
Sparse embeddings of data form an attractive class due to their inherent interpretability: Every dimension is tied to a term in some vocabulary, making it easy to visually decipher the latent space. Sparsity, however, poses unique…
Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional…
Variable selection for sparse linear regression is the problem of finding, given an m x p matrix B and a target vector y, a sparse vector x such that Bx approximately equals y. Assuming a standard complexity hypothesis, we show that no…
The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest…
We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…
In this paper we revisit the sparse multiple measurement vector (MMV) problem where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem has received increasing interest as an…
Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, we work with a subset of $b$…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…
This paper revisits cluster-based retrieval that partitions the inverted index into multiple groups and skips the index partially at cluster and document levels during online inference using a learned sparse representation. It proposes an…
We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…
Text retrieval using learned sparse representations of queries and documents has, over the years, evolved into a highly effective approach to search. It is thanks to recent advances in approximate nearest neighbor search-with the emergence…
The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…
Structured sparsity has been proposed as an efficient way to prune the complexity of modern Machine Learning (ML) applications and to simplify the handling of sparse data in hardware. The acceleration of ML models - for both training and…
We consider the synthesis problem of Compressed Sensing - given s and an MXn matrix A, extract from it an mXn submatrix A', certified to be s-good, with m as small as possible. Starting from the verifiable sufficient conditions of…
Large language model (LLM) pruning with fixed N:M structured sparsity significantly limits the expressivity of the sparse model, yielding sub-optimal performance. In contrast, supporting multiple N:M patterns to provide sparse…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…