Data networks
The competitiveness of on-line assignments
Journal of Algorithms
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Improved bicriteria existence theorems for scheduling
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Fairness in routing and load balancing
Journal of Computer and System Sciences - Special issue on Internet algorithms
Combining fairness with throughout: online routing with multiple objectives
Journal of Computer and System Sciences - Special issue on Internet algorithms
Developments from a June 1996 seminar on Online algorithms: the state of the art
All-norm approximation algorithms
Journal of Algorithms
Approximate majorization and fair online load balancing
ACM Transactions on Algorithms (TALG)
Fairness Measures for Resource Allocation
SIAM Journal on Computing
Operations Research Letters
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We revisit from a fairness point of view the problem of online load balancing in the restricted assignment model and the 1-驴 model. We consider both a job-centric and a machine-centric view of fairness, as proposed by Goel et al. (In: Symposium on discrete algorithms, pp. 384---390, 2005). These notions are equivalent to the approximate notion of prefix competitiveness proposed by Kleinberg et al. (In: Proceedings of the 40th annual symposium on foundations of computer science, p. 568, 2001), as well as to the notion of approximate majorization, and they generalize the well studied notion of max-min fairness.We resolve a question posed by Goel et al. (In: Symposium on discrete algorithms, pp. 384---390, 2005) proving that the greedy strategy is globally O(log驴m)-fair, where m denotes the number of machines. This result improves upon the analysis of Goel et al. (In: Symposium on discrete algorithms, pp. 384---390, 2005) who showed that the greedy strategy is globally O(log驴n)-fair, where n is the number of jobs. Typically, n驴m, and therefore our improvement is significant. Our proof matches the known lower bound for the problem with respect to the measure of global fairness.The improved bound is obtained by analyzing, in a more accurate way, the more general restricted assignment model studied previously in Azar et al. (J. Algorithms 18:221---237, 1995). We provide an alternative bound which is not worse than the bounds of Azar et al. (J. Algorithms 18:221---237, 1995), and it is strictly better in many cases. The bound we prove is, in fact, much more general and it bounds the load on any prefix of most loaded machines. As a corollary from this more general bound we find that the greedy algorithm results in an assignment that is globally O(log驴m)-balanced. The last result generalizes the previous result of Goel et al. (In: Symposium on discrete algorithms, pp. 384---390, 2005) who proved that the greedy algorithm yields an assignment that is globally O(log驴m)-balanced for the 1-驴 model.