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Optimization Problems in Fair Division Theory
Published in George Anastassiou, Handbook of Analytic-Computational Methods in Applied Mathematics, 2019
so aii(ϕ) ≥ si. Hence an envy-free allocation is fair, as long as the same system of weights is used. Thus, for a given s, we conclude () ε˜(s)⊂ε(s)⊂F(s).
An online fair resource allocation solution for fog computing
Published in International Journal of Parallel, Emergent and Distributed Systems, 2022
Jia He Sun, Salimur Choudhury, Kai Salomaa
Fairness between users who request tasks can be evaluated by Dominant Resource Fairness (DRF), an index developed by Ghodsi et al. in 2011 [12]. The DRF scheme is a multi-resource generalisation of max–min fairness. According to the DRF scheme, in a multi-resource environment where tasks have heterogeneous resource demands, a user's dominant share is the maximum global share that the user has been allocated of any resource. In essence, the DRF scheme aims to have all users have equal dominant share values in any allocation. In their publication defining the DRF scheme, Godhsi et al. [12] considered many other fairness schemes including Asset Fairness and Competitive Equilibrium from Equal Incomes (CEEI). Asset Fairness aims to equalise the aggregate resource value allocated to each user assuming that equal shares of different resources are worth the same. That is, 1% of resource 1 is equivalent to 1% of resource 2. CEEI, the preferred method of fair resource allocation in microeconomic theory [12], initially allocates of each resource to each user and subsequently, each user can trade their resources with other users. Godhsi et al. [12] found that the DRF scheme is the only fairness scheme that satisfies the following four key qualities: Sharing Incentive: every task's allocation is better than that obtained by dividing every resource evenly between tasksStrategy-proof: tasks cannot get better allocation by lying about their requirementsPareto-efficiency: all available resources are allocated subject to satisfying the other properties, and without preempting existing allocationsEnvy Free: no task prefers the allocation of another task