Publications

Proportional fairness criteria inspired by democratic ideals of proportional representation have received growing attention in the clustering literature. Prior work has investigated them in two separate paradigms. Chen et al. [ICML 2019] study centroid clustering, in which each data point's loss is determined by its distance to a representative point (centroid) chosen in its cluster. Caragiannis et al. [NeurIPS 2024] study non-centroid clustering, in which each data point's loss is determined by its maximum distance to any other data point in its cluster. We generalize both paradigms to introduce semi-centroid clustering, in which each data point's loss is a combination of its centroid and non-centroid losses, and study two proportional fairness criteria -- the core and, its relaxation, fully justified representation (FJR). Our main result is a novel algorithm which achieves a constant approximation to the core, in polynomial time, even when the distance metrics used for centroid and non-centroid loss measurements are different. We also derive improved results for more restricted loss functions and the weaker FJR criterion, and establish lower bounds in each case.

Stability has been a foundational criterion for two-sided matching. When agents on one side have weak preferences involving indifferences, the seminal work of Kesten and Ünver [2015] proposes the Fractional Deferred Acceptance (FDA) algorithm for computing a fractional matching that satisfies (ex ante) stability along with a fairness criterion that ensures no discrimination among (equally-preferred) agents on one side. We show that their algorithm can actually fail to terminate, refuting their claim of (polynomial-time) termination. Using substantially new algorithmic ideas, we develop an algorithm, Doubly-Fractional Deferred Acceptance (DFDA), which can handle agents on both sides exhibiting indifferences and, in polynomial time, compute a fractional matching satisfying ex ante stability and no ex ante discrimination among agents on both sides, thus fixing and superseding the result of Kesten and Ünver [2015].

We study temporal fair division, whereby a set of agents are allocated a (possibly different) set of goods on each day for a period of days. We study this setting, as well as a number of its special cases formed by the restrictions to two agents, same goods on each day, identical preferences, or combinations thereof, and chart out the landscape of achieving two types of fairness guarantees simultaneously: fairness on each day (per day) and fairness over time (up to each day, or the weaker version, overall). In the most general setting, we prove that there always exists an allocation that is stochastically-dominant envy-free up to one good (SD-EF1) per day and proportional up to one good (PROP1) overall, and when all the agents have identical preferences, we show that SD-EF1 per day and SD-EF1 overall can be guaranteed. For the case of two agents, we prove that SD-EF1 per day and EF1 up to each day can be guaranteed using an envy balancing technique. We provide counterexamples for other combinations that establish our results as among the best guarantees possible, but also leaving open some tantalizing questions.

Fairness and efficiency have become the pillars of modern fair division research, but prior work on achieving both simultaneously is largely limited to the unconstrained setting. We study fair and efficient allocations of indivisible goods under additive valuations and various types of allocation feasibility constraints, and demonstrate the unreasonable effectiveness of the maximum Nash welfare (MNW) solution in this previously uncharted territory. Our main result is that MNW allocations are 1/2-envy-free up to one good (EF1) and Pareto optimal under the broad family of (arbitrary) matroid constraints. We extend these guarantees to complete MNW allocations for base-orderable matroid constraints, and to a family of non-matroidal constraints (which includes balancedness) using a novel "alternate worlds" technique. We establish tightness of our results by providing counterexamples for the satisfiability of certain stronger desiderata, but show an improved result for the special case of goods with copies (Gafni et al. 2023). Finally, we also establish novel best-of-both-worlds guarantees for goods with copies and balancedness.