Related papers: Fair and Square: Cake-Cutting in Two Dimensions
This paper explores the fair allocation of indivisible items in a multidimensional setting, motivated by the need to address fairness in complex environments where agents assess bundles according to multiple criteria. Such multidimensional…
We explore an instance of the question of partitioning a polygon into pieces, each of which is as ``circular'' as possible, in the sense of having an aspect ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters of…
In classic fair division problems such as cake cutting and rent division, envy-freeness requires that each individual (weakly) prefer his allocation to anyone else's. On a conceptual level, we argue that envy-freeness also provides a…
We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on…
The field of fair machine learning aims to ensure that decisions guided by algorithms are equitable. Over the last decade, several formal, mathematical definitions of fairness have gained prominence. Here we first assemble and categorize…
Recently, Landau, Reid and Yershov provided a novel solution to the problem of redistricting. Instead of trying to ensure fairness by restricting the shape of the possible maps or by assigning the power to draw the map to nonbiased…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
This paper studies two families of constraints for two-dimensional and multidimensional arrays. The first family requires that a multidimensional array will not contain a cube of zeros of some fixed size and the second constraint imposes…
We study the problem of perfect tiling in the plane and exploring the possibility of tiling a rectangle using integral distinct squares. Assume a set of distinguishable squares (or equivalently a set of distinct natural numbers) is given,…
We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across…
We prove an $\Omega(n^2)$ lower bound on the query complexity of local proportionality in the Robertson-Webb cake-cutting model. Local proportionality requires that each agent prefer their allocation to the average of their neighbors'…
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be…
We study the fair division of indivisible goods with conflicts between pairs of goods, represented by a graph $G = (V, E)$. We consider ``soft'' conflicts: assigning two adjacent goods to the same agent is allowed, but we seek allocations…
We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering $n$ points with $k$ centers, we define fairness as proportionality to mean that any $n/k$…
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to…
In this paper, we study the problem of splitting fairly bundles of items. We show that given $n$ bundles with $m$ kinds of items in them, it is possible to distribute the value of each kind of item fairly among $r$ persons by breaking apart…
We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to…
The division of goods in the online realm poses opportunities and challenges. While innovative mechanisms can be developed, uncertainty about the future may hinder effective solutions. This project aims to explore fair distribution models…