Related papers: An approximation algorithm for Uniform Capacitated…

We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…

\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…

Algorithms with predictions have attracted much attention in the last years across various domains, including variants of facility location, as a way to surpass traditional worst-case analyses. We study the $k$-facility location mechanism…

We propose a first-order augmented Lagrangian algorithm (FALC) to solve the composite norm minimization problem min |sigma(F(X)-G)|_alpha + |C(X)- d|_beta subject to A(X)-b in Q; where sigma(X) denotes the vector of singular values of X,…

A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.…

For the constrained 2-means problem, we present a $O\left(dn+d({1\over\epsilon})^{O({1\over \epsilon})}\log n\right)$ time algorithm. It generates a collection $U$ of approximate center pairs $(c_1, c_2)$ such that one of pairs in $U$ can…

Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…

This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…

Fair clustering enjoyed a surge of interest recently. One appealing way of integrating fairness aspects into classical clustering problems is by introducing multiple covering constraints. This is a natural generalization of the robust (or…

In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

We introduce a problem that is a common generalization of the uncapacitated facility location and minimum latency (ML) problems, where facilities need to be opened to serve clients and also need to be sequentially activated before they can…

In fully-dynamic consistent clustering, we are given a finite metric space $(M,d)$, and a set $F\subseteq M$ of possible locations for opening centers. Data points arrive and depart, and the goal is to maintain an approximately optimal…

Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…

The Johnson-Lindenstrauss (JL) Lemma introduced the concept of dimension reduction via a random linear map, which has become a fundamental technique in many computational settings. For a set of $n$ points in $\mathbb{R}^d$ and any fixed…

We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group…

We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns…