Related papers: Constant-Factor Distortion Mechanisms for $k$-Comm…

In the well-studied metric distortion problem in social choice, we have voters and candidates located in a shared metric space, and the objective is to design a voting rule that selects a candidate with minimal total distance to the voters.…

We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…

We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…

The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds.…

The Kemeny aggregation problem consists of computing the consensus rankings of an election with respect to the well-known Kemeny-Young voting method. These consensus rankings satisfy various fundamental properties and are the geometric…

In this work, we define and solve the Fair Top-k Ranking problem, in which we want to determine a subset of k candidates from a large pool of n >> k candidates, maximizing utility (i.e., select the "best" candidates) subject to group…

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…

We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…

In the standard planar $k$-center clustering problem, one is given a set $P$ of $n$ points in the plane, and the goal is to select $k$ center points, so as to minimize the maximum distance over points in $P$ to their nearest center. Here we…

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…

We consider the problem of electing a committee of $k$ candidates, subject to some constraints as to what this committee is supposed to look like. In our framework, the candidates are given labels as an abstraction of a politician's…

The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum…

We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each…

Gerrymandering is a practice of manipulating district boundaries and locations in order to achieve a political advantage for a particular party. Lewenberg, Lev, and Rosenschein [AAMAS 2017] initiated the algorithmic study of a…

Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in \mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$, where $d(x,C)$…

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…

Strategic manipulation of elections is typically studied in the context of promoting individual candidates. In parliamentary elections, however, the focus shifts: voters may care more about the overall governing coalition than the…

Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population's opinion? We present a positive answer…

We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on…