Related papers: Dynamic Range Majority Data Structures
In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive…
In list-decodable subspace recovery, the input is a collection of $n$ points $\alpha n$ (for some $\alpha \ll 1/2$) of which are drawn i.i.d. from a distribution $\mathcal{D}$ with a isotropic rank $r$ covariance $\Pi_*$ (the…
A fundamental problem in data management is to find the elements in an array that match a query. Recently, learned indexes are being extensively used to solve this problem, where they learn a model to predict the location of the items in…
Effective decision making in partially observable environments requires compressing long interaction histories into informative representations. We introduce Descriptive History Representations (DHRs): sufficient statistics characterized by…
The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…
We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results.…
We study the non-overlapping indexing problem: Given a text T, preprocess it so that you can answer queries of the form: given a pattern P, report the maximal set of non-overlapping occurrences of P in T. A generalization of this problem is…
The abundant semi-structured data on the Web, such as HTML-based tables and lists, provide commercial search engines a rich information source for question answering (QA). Different from plain text passages in Web documents, Web tables and…
We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of…
We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs. For instance, it is known how to maintain a 1/2-approximate matching in $\log^{O(1)} n$…
Given a set $ P $ of $n$ points and a set $ H $ of $n$ half-planes in the plane, we consider the problem of computing a smallest subset of points such that each half-plane contains at least one point of the subset. The previously best…
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights and characterization for different iterative process, and…
We study the Fr\'echet queries problem. It is a data structure problem, where we are given a set $S$ of $n$ polygonal curves and a distance threshold $\rho$. The data structure should support queries with a polygonal curve $q$ for the…
We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in $O(\log^2n/\log\log n)$ amortized time and connectivity queries in $O(\log n/\log\log n)$ worst-case…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks us to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
We design the first learned index that solves the dictionary problem with time and space complexity provably better than classic data structures for hierarchical memories, such as B-trees, and modern learned indexes. We call our solution…
Dynamic data selection aims to accelerate training with lossless performance. However, reducing training data inherently limits data diversity, potentially hindering generalization. While data augmentation is widely used to enhance…