相关论文: How to cut a cake with a gram matrix
We analyze lower bounds for the number of envy-free divisions, in the classical Woodall-Stormquist setting and in a non-classical case, when envy-freeness is combined with the equipartition of a measure. 1. In the first scenario, there are…
We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good…
The classic cake-cutting problem provides a model for addressing the fair and efficient allocation of a divisible, heterogeneous resource among agents with distinct preferences. Focusing on a standard formulation of cake cutting, in which…
This paper deals with two problems about splitting fairly a path with colored vertices, where "fairly" means that each part contains almost the same amount of vertices in each color. Our first result states that it is possible to remove one…
Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…
Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and…
We propose an online form of the cake cutting problem. This models situations where players arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the…
Fairness is an important objective throughout society. From the distribution of limited goods such as education, over hiring and payment, to taxes, legislation, and jurisprudence. Due to the increasing importance of machine learning…
A pizza is a pair of planar convex bodies $A\subseteq B$,where $B$ represents the dough and $A$ the topping of the pizza. A partition of a pizza by straight lines is a succession of double operations:a cut by a full straight line, followed…
We study the problem of fair classification within the versatile framework of Dwork et al. [ITCS '12], which assumes the existence of a metric that measures similarity between pairs of individuals. Unlike earlier work, we do not assume that…
We study the classic problem of \emph{fairly} dividing a heterogeneous and divisible resource -- modeled as a line segment $[0,1]$ and typically called as a \emph{cake} -- among $n$ agents. This work considers an interesting variant of the…
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…
Envy-freeness is one of the most prominent fairness concepts in the allocation of indivisible goods. Even though trivial envy-free allocations always exist, rich literature shows this is not true when one additionally requires some…
This work develops algorithmic results for the classic cake-cutting problem in which a divisible, heterogeneous resource (modeled as a cake) needs to be partitioned among agents with distinct preferences. We focus on a standard formulation…
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…
Alice and Bob want to cut a cake; however, in contrast to the usual problems of fair division, they want to cut it unfairly. More precisely, they want to cut it in ratio $(a:b)$. (We can assume gcd(a,b)=1.) Let f(a,b) be the number of cuts…
In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.
We propose an online form of the cake cutting problem. This models situations where agents arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the…
We consider the problem of dividing items between individuals in a way that is fair both in the sense of distributional fairness and in the sense of not having disparate impact across protected classes. An important existing mechanism for…
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…