相关论文: An $\Omega(n \log n)$ Randomized Lower Bound for C…
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 study the query complexity of cake cutting and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing connected…
In this article we study a cake cutting problem. More precisely, we study symmetric fair division algorithms, that is to say we study algorithms where the order of the players do not influence the value obtained by each player. In the first…
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…
The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…
We study searching and sorting in rounds motivated by a fair division question: given a cake cutting problem with $n$ players, compute a fair allocation in at most $k$ rounds of interaction with the players. Rounds interpolate between the…
In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson-Webb model but he or she can only perform algebraic operations as in the Blum-Shub-Smale…
We study the proportional chore division problem where a protocol wants to divide an undesirable object, called chore, among $n$ different players. The goal is to find an allocation such that the cost of the chore assigned to each player be…
An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among $n$ players who value pieces according to…
We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show…
We study the disproportionate version of the classical cake-cutting problem: how efficiently can we divide a cake, here $[0,1]$, among $n$ agents with different demands $\alpha_1, \alpha_2, \dots, \alpha_n$ summing to $1$? When all the…
In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other agents. We introduce a variant of the…
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for…
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…
In this paper, we show algorithms for solving the cake-cutting problem in sublinear-time. More specifically, we preassign (simple) fair portions to o(n) players in o(n)-time, and minimize the damage to the rest of the players. All currently…
The classical cake cutting problem studies how to find fair allocations of a heterogeneous and divisible resource among multiple agents. Two of the most commonly studied fairness concepts in cake cutting are proportionality and…
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to…
The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division…
Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece…
In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…