Related papers: Optimal Clustering with Noisy Queries via Multi-Ar…
We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…
In this paper, we consider non-smooth convex optimization with a zeroth-order oracle corrupted by symmetric stochastic noise. Unlike the existing high-probability results requiring the noise to have bounded $\kappa$-th moment with $\kappa…
We study a variant of the canonical k-center problem over a set of vertices in a metric space, where the underlying distances are apriori unknown. Instead, we can query an oracle which provides noisy/incomplete estimates of the distance…
The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…
Maximum diversity aims at selecting a diverse set of high-quality objects from a collection, which is a fundamental problem and has a wide range of applications, e.g., in Web search. Diversity under a uniform or partition matroid constraint…
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its…
We first consider the problem of learning $k$-parities in the on-line mistake-bound model: given a hidden vector $x \in \{0,1\}^n$ with $|x|=k$ and a sequence of "questions" $a_1, a_2, ...\in \{0,1\}^n$, where the algorithm must reply to…
We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
The clique problems, including $k$-CLIQUE and Triangle Finding, form an important class of computational problems; the former is an NP-complete problem, while the latter directly gives lower bounds for Matrix Multiplication. A number of…
Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
We consider the problem of latent bandits with cluster structure where there are multiple users, each with an associated multi-armed bandit problem. These users are grouped into \emph{latent} clusters such that the mean reward vectors of…
Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
We consider the problem of locating a signal whose frequencies are "off grid" and clustered in a narrow band. Given noisy sample access to a function $g(t)$ with Fourier spectrum in a narrow range $[f_0 - \Delta, f_0 + \Delta]$, how…
Clustering with capacity constraints is a fundamental problem that attracted significant attention throughout the years. In this paper, we give the first FPT constant-factor approximation algorithm for the problem of clustering points in a…
A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…
In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n \log n)$…