我们研究无嫉妒机制调度任务不相关的机器（代理），大约最小化的完工时间。对于不可分割的任务，我们提出了一个无嫉妒的多时间机制，近似的最小完工时间内的一个因素$O(\log m)$，其中$m$是机器的数量。我们还证明了$Ω(\log m / \log\log m)$的一个下界。这改进了Hartline { \sl et al.}给出$(m+1)/2$的上限和$2-1/m$的下限的\cite{Ahuva:2008}。对于可分割的任务，我们表明，总是存在一个嫉妒免费多时间机制与最佳的完工时间。
英文摘要：
We study envy-free mechanisms for scheduling tasks on unrelated machines (agents) that approximately minimize the makespan. For indivisible tasks, we put forward an envy-free poly-time mechanism that approximates the minimal makespan to within a factor of $O(\log m)$, where $m$ is the number of machines. We also show a lower bound of $Ω(\log m / \log\log m)$. This improves the recent result of Hartline {\sl et al.} \cite{Ahuva:2008} who give an upper bound of $(m+1)/2$, and a lower bound of $2-1/m$. For divisible tasks, we show that there always exists an envy-free poly-time mechanism with optimal makespan.
Several relaxations of envy-freeness, tailored to fair division in settings with indivisible goods, have been introduced within the last decade. Due to the lack of general existence results for most of these concepts, great attention has been paid to establishing approximation guarantees. In this work, we propose a simple algorithm that is universally fair in the sense that it returns allocations that have good approximation guarantees with respect to four such fairness notions at once. In particular, this is the first algorithm achieving a $(ϕ-1)$-approximation of envy-freeness up to any good…
我们认为优先级自由拍卖收入和福利最大化时，代理人有一个共同的预算。我们考虑的抽象环境是有一个向下封闭的和对称的可行性约束的代理服务的概率。这些环境包括位置拍卖，其中具有降低的点击率的位置被拍卖给广告商。我们将Hartline和Yan（2011）的无嫉妒基准推广和表征到有预算的环境中，并表征福利和收入的最佳无嫉妒结果。我们给出了近似这些基准的无先验机制。在我们的机制的一个组成部分是一个成交拍卖的位置拍卖环境。该拍卖是Dobzinski et al.（2008）的多单位成交拍卖的推广，也是Goel et al.（2012）的多面体成交拍卖的特例。对于福利最大化，我们表明，这种成交拍卖是一个很好的近似的嫉妒无最优福利的位置拍卖环境。对于利润最大化，我们推广了Fiat等人（2002）的随机抽样利润提取拍卖，用于数字商品，以给出对称下闭环境中无嫉妒最优收入的10.0近似值。即使没有预算，利润最大化问题也很有趣，我们的机制是一个7.5近似，改进了Ha和Hartline（2012）的30.4界限。
The Nash social welfare (NSW) is a well-known social welfare measurement that balances individual utilities and the overall efficiency. In the context of fair allocation of indivisible goods, it has been shown by Caragiannis et al. (EC 2016 and TEAC 2019) that an allocation maximizing the NSW is envy-free up to one good (EF1). In this paper, we are interested in the fairness of the NSW in a budget-feasible allocation problem, in which each item has a cost that will be incurred to the agent it is allocated to, and each agent has a budget constraint on the total cost of items she receives. We sh…
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 this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where i…
In the budget-feasible allocation problem, a set of items with varied sizes and values are to be allocated to a group of agents. Each agent has a budget constraint on the total size of items she can receive. The goal is to compute a feasible allocation that is envy-free (EF), in which the agents do not envy each other for the items they receive, nor do they envy a charity, who is endowed with all the unallocated items. Since EF allocations barely exist even without budget constraints, we are interested in the relaxed notion of envy-freeness up to one item (EF1). The computation of both exact a…
The Nisan-Ronen conjecture states that no truthful mechanism for makespan-minimization when allocating $m$ tasks to $n$ unrelated machines can have approximation ratio less than $n$. Over more than two decades since its formulation, little progress has been made in resolving it and the best known lower bound is still a small constant. This work makes progress towards validating the conjecture by showing a lower bound of $1+\sqrt{n-1}$.
We study the problem of dividing a multi-layered cake under non-overlapping constraints. This problem, recently proposed by Hosseini et al. (IJCAI, 2020), captures several natural scenarios such as the allocation of multiple facilities over time where each agent can utilize at most one facility simultaneously, and the allocation of tasks over time where each agent can perform at most one task simultaneously. We establish the existence of an envy-free multi-division that is both non-overlapping and contiguous within each layer when the number of agents is a prime power and the number of layers …
School of Informatics, Aristotle University of Thessaloniki（阿波罗尼奥斯大学信息学院）；Archimedes, Athena Research Center（阿基米德，雅典研究中心）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）；Institute of Computer Science, Goethe University Frankfurt（法兰克福歌德大学计算机科学研究所）
In their seminal paper that initiated the field of algorithmic mechanism design, \citet{NR99} studied the problem of designing strategyproof mechanisms for scheduling jobs on unrelated machines aiming to minimize the makespan. They provided a strategyproof mechanism that achieves an $n$-approximation and they made the bold conjecture that this is the best approximation achievable by any deterministic strategyproof scheduling mechanism. After more than two decades and several efforts, $n$ remains the best known approximation and very recent work by \citet{CKK21} has been able to prove an $Ω(\sq…
We consider the scheduling problem on $n$ strategic unrelated machines when no payments are allowed, under the objective of minimizing the makespan. We adopt the model introduced in [Koutsoupias, Theory Comput. Syst. (2014)] where a machine is bound by her declarations in the sense that if she is assigned a particular job then she will have to execute it for an amount of time at least equal to the one she reported, even if her private, true processing capabilities are actually faster. We provide a (non-truthful) randomized algorithm whose pure Price of Anarchy is arbitrarily close to $1$ for t…
