Related papers: Fair and Square: Cake-cutting in Two Dimensions
A cake has to be divided fairly among $n$ agents. When all agents have equal entitlements, it is known that such a division can be implemented with $n-1$ cuts. When agents may have different entitlements, the paper shows that at least $2 n…
A collection of objects, some of which are good and some are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely…
Given an edge-colored graph, the goal of the proportional fair matching problem is to find a maximum weight matching while ensuring proportional representation (with respect to the number of edges) of each color. The colors may correspond…
In Fair AI literature, the practice of maliciously creating unfair models that nevertheless satisfy fairness constraints is known as "cherry-picking". A cherry-picking model is a model that makes mistakes on purpose, selecting bad…
We study the envy-free cake-cutting problem for $d+1$ players with $d$ cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a $\theta(({1\over\epsilon})^{d-1})$ time matching bound for…
Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact…
We consider the classic cake-cutting problem of producing fair allocations for $n$ agents, in the Robertson-Webb query model. In this model, it is known that: (i) proportional allocations can be computed using $O(n \log n)$ queries, and…
In this article, the issue of choice cuts made to a rectangular region are considered and explored. Results show that this problem is not trivial. Outcomes for teaching and learning are considered.
The allocation of resources among multiple agents is a fundamental problem in both economics and computer science. In these settings, fairness plays a crucial role in ensuring social acceptability and practical implementation of resource…
We revisit the classic problem of fair division from a mechanism design perspective, using {\em Proportional Fairness} as a benchmark. In particular, we aim to allocate a collection of divisible items to a set of agents while incentivizing…
There is a heterogeneous resource that contains both good parts and bad parts, for example, a cake with some parts burnt, a land-estate with some parts heavily taxed, or a chore with some parts fun to do. The resource has to be divided…
Envy-free cake-cutting protocols procedurally divide an infinitely divisible good among a set of agents so that no agent prefers another's allocation to their own. These protocols are highly complex and difficult to prove correct. Recently,…
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…
The theory of algorithmic fair allocation is within the center of multi-agent systems and economics in the last decade due to its industrial and social importance. At a high level, the problem is to assign a set of items that are either…
Fair resource allocation is an important problem in many real-world scenarios, where resources such as goods and chores must be allocated among agents. In this survey, we delve into the intricacies of fair allocation, focusing specifically…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Many interesting problems in the Internet industry can be framed as a two-sided marketplace problem. Examples include search applications and recommender systems showing people, jobs, movies, products, restaurants, etc. Incorporating…
Austin's moving knife procedure was originally introduced to find a consensus division of an interval/circular cake between two agents, each of whom believes that they receive exactly half of the cake. We generalise this in two ways: we…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this…