arXiv subjects

Annika Hennes

Publications and source records attributed to Annika Hennes.

5 recordsLinked to original sources

arXiv2026

Exact ratio preservation via outliers for fair $k$-center clustering

We study the $k$-center clustering problem under demographic fairness constraints, where the point set is partitioned into groups, and the aim is to compute clusters that exhibit a given group proportion. Previous work in this direction assumes that the entire point set already respects the desired proportions or uses relaxed notions of fairness. In this work, we propose a model that facilitates the creation of clusters that exactly match given target ratios, even when the input point set does not. We combine the well-known fair clustering model initiated by Chierichetti, Kumar, Lattanzi, and Vassilvitskii (NeurIPS 2017) with the notion of outliers to obtain a practical combinatorial framework that provides constant-factor approximate solutions for all proportion settings from $1:1$ for two groups to $t_1:t_2:\ldots:t_m$ for $m\geq 2$ groups, where $t_1,\ldots,t_m$ are integers. We implement and evaluate our algorithms, compare different variants, and provide evidence of the practicability of this approach.

cs.DS↗

arXiv2026

Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means

We study discrete k-clustering problems in general metric spaces that are constrained by a combination of two different fairness conditions within the demographic fairness model. Given a metric space (P,d), where every point in P is equipped with a protected attribute, and a number k, the goal is to partition P into k clusters with a designated center each, such that a center-based objective function is minimized and the attributes are fairly distributed with respect to the following two fairness concepts: 1) group fairness: We aim for clusters with balanced numbers of attributes by specifying lower and upper bounds for the desired attribute proportions. 2) diverse center selection: Clusters have natural representatives, i.e., their centers. We ask for a balanced set of representatives by specifying the desired number of centers to choose from each attribute. Dickerson, Esmaeili, Morgenstern and Zhang (2023) denote the combination of these two constraints as doubly constrained fair clustering. They present algorithms whose guarantees depend on the best known approximation factors for either of these problems. Currently, this implies an 8-approximation with a small additive violation on the group fairness constraint. For k-center, we improve this approximation factor to 4 with a small additive violation. This guarantee also depends on the currently best algorithm for DS-fair k-center given by Jones, Nguyen and Nguyen (2020). For k-median and k-means, we propose the first constant-factor approximation algorithms. Our algorithms transform a solution that satisfies diverse center selection into a doubly constrained fair clustering using an LP-based approach. Furthermore, our results are generalizable to other center-selection constraints, such as matroid k-clustering and knapsack constraints.

cs.DS↗

arXiv2024

FPT Approximations for Fair $k$-Min-Sum-Radii

We consider the $k$-min-sum-radii ($k$-MSR) clustering problem with fairness constraints. The $k$-min-sum-radii problem is a mixture of the classical $k$-center and $k$-median problems. We are given a set of points $P$ in a metric space and a number $k$ and aim to partition the points into $k$ clusters, each of the clusters having one designated center. The objective to minimize is the sum of the radii of the $k$ clusters (where in $k$-center we would only consider the maximum radius and in $k$-median we would consider the sum of the individual points' costs). Various notions of fair clustering have been introduced lately, and we follow the definitions due to Chierichetti, Kumar, Lattanzi and Vassilvitskii [NeurIPS 2017] which demand that cluster compositions shall follow the proportions of the input point set with respect to some given sensitive attribute. For the easier case where the sensitive attribute only has two possible values and each is equally frequent in the input, the aim is to compute a clustering where all clusters have a 1:1 ratio with respect to this attribute. We call this the 1:1 case. There has been a surge of FPT-approximation algorithms for the $k$-MSR problem lately, solving the problem both in the unconstrained case and in several constrained problem variants. We add to this research area by designing an FPT $(6+ε)$-approximation that works for $k$-MSR under the mentioned general fairness notion. For the special 1:1 case, we improve our algorithm to achieve a $(3+ε)$-approximation.

cs.DS↗

arXiv2024

Approximating Fair $k$-Min-Sum-Radii in Euclidean Space

The $k$-center problem is a classical clustering problem in which one is asked to find a partitioning of a point set $P$ into $k$ clusters such that the maximum radius of any cluster is minimized. It is well-studied. But what if we add up the radii of the clusters instead of only considering the cluster with maximum radius? This natural variant is called the $k$-min-sum-radii problem. It has become the subject of more and more interest in recent years, inspiring the development of approximation algorithms for the $k$-min-sum-radii problem in its plain version as well as in constrained settings. We study the problem for Euclidean spaces $\mathbb{R}^d$ of arbitrary dimension but assume the number $k$ of clusters to be constant. In this case, a PTAS for the problem is known (see Bandyapadhyay, Lochet and Saurabh, SoCG, 2023). Our aim is to extend the knowledge base for $k$-min-sum-radii to the domain of fair clustering. We study several group fairness constraints, such as the one introduced by Chierichetti et al. (NeurIPS, 2017). In this model, input points have an additional attribute (e.g., colors such as red and blue), and clusters have to preserve the ratio between different attribute values (e.g., have the same fraction of red and blue points as the ground set). Different variants of this general idea have been studied in the literature. To the best of our knowledge, no approximative results for the fair $k$-min-sum-radii problem are known, despite the immense amount of work on the related fair $k$-center problem. We propose a PTAS for the fair $k$-min-sum-radii problem in Euclidean spaces of arbitrary dimension for the case of constant $k$. To the best of our knowledge, this is the first PTAS for the problem. It works for different notions of group fairness.

cs.DS↗

arXiv2023

Markov Decision Processes with Time-Varying Geometric Discounting

Canonical models of Markov decision processes (MDPs) usually consider geometric discounting based on a constant discount factor. While this standard modeling approach has led to many elegant results, some recent studies indicate the necessity of modeling time-varying discounting in certain applications. This paper studies a model of infinite-horizon MDPs with time-varying discount factors. We take a game-theoretic perspective -- whereby each time step is treated as an independent decision maker with their own (fixed) discount factor -- and we study the subgame perfect equilibrium (SPE) of the resulting game as well as the related algorithmic problems. We present a constructive proof of the existence of an SPE and demonstrate the EXPTIME-hardness of computing an SPE. We also turn to the approximate notion of $ε$-SPE and show that an $ε$-SPE exists under milder assumptions. An algorithm is presented to compute an $ε$-SPE, of which an upper bound of the time complexity, as a function of the convergence property of the time-varying discount factor, is provided.

cs.AI↗