The price of envy-freeness in machine scheduling - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Theoretical Computer Science Année : 2016

The price of envy-freeness in machine scheduling

Résumé

We consider k-envy-free assignments for scheduling problems in which the completion time of each machine is not k times larger than the one she could achieve by getting the jobs of another machine, for a given factor . We introduce and investigate the notion of price of k-envy-freeness, defined as the ratio between the makespan of the best k-envy-free assignment and that of an optimal allocation achievable without envy-freeness constraints. We provide exact or asymptotically tight bounds on the price of k-envy-freeness for all the basic scheduling models, that is unrelated, related and identical machines. Moreover, we show how to efficiently compute such allocations with a worsening multiplicative factor being at most the best approximation ratio for the minimum makespan problem guaranteed by a polynomial time algorithm for each specific model. Finally, we extend our results to the case of restricted assignments and to the objective of minimizing the sum of the completion times of all the machines.

Dates et versions

hal-02089421 , version 1 (03-04-2019)

Identifiants

Citer

Vittorio Bilò, Angelo Fanelli, Michele Flammini, Gianpiero Monaco, Luca Moscardelli. The price of envy-freeness in machine scheduling. Theoretical Computer Science, 2016, 613, pp.65-78. ⟨10.1016/j.tcs.2015.10.046⟩. ⟨hal-02089421⟩
52 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More