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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…
In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea than the ''Full independence model'' used in the study of…
The classic cake-cutting problem provides a model for addressing fair and efficient allocation of a divisible, heterogeneous resource (metaphorically, the cake) among agents with distinct preferences. Focusing on a standard formulation of…
We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized…
We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation in order to receive a better allocation. A…
We consider the problem of fairly dividing a two dimensional heterogeneous good among multiple players. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols primarily…
We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in…
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…
Motivated by fairness requirements in communication networks, we introduce a natural variant of the online paging problem, called \textit{min-max} paging, where the objective is to minimize the maximum number of faults on any page. While…
We investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents who may have different entitlements. We characterize the existence of a connected strongly-proportional allocation…
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…
We consider the classical cake-cutting problem where we wish to fairly divide a heterogeneous resource, often modeled as a cake, among interested agents. Work on the subject typically assumes that the cake is represented by an interval. In…
In this note we study a problem of fair division in the absence of full information. We give an algorithm which solves the following problem: n $\ge$ 2 persons want to cut a cake into n shares so that each person will get at least 1/n of…
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…
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…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the…
We consider the classic problem of fairly dividing a heterogeneous good ("cake") among several agents with different valuations. Classic cake-cutting procedures either allocate each agent a collection of disconnected pieces, or assume that…
We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality to this…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…