TY - JOUR

T1 - Fair online load balancing

AU - Buchbinder, Niv

AU - Naor, Joseph

N1 - Funding Information:
This work was partly supported by ISF grant 1366/07.

PY - 2013/2

Y1 - 2013/2

N2 - We revisit from a fairness point of view the problem of online load balancing in the restricted assignment model and the 1-∞ 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 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 n)-fair, where n is the number of jobs. Typically, nâ‰, 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 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 m)-balanced for the 1-∞ model.

AB - We revisit from a fairness point of view the problem of online load balancing in the restricted assignment model and the 1-∞ 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 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 n)-fair, where n is the number of jobs. Typically, nâ‰, 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 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 m)-balanced for the 1-∞ model.

KW - Competitive analysis

KW - Fairness

KW - Load balancing

KW - Online algorithms

KW - Restricted assignment

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=84874109285&partnerID=8YFLogxK

U2 - 10.1007/s10951-011-0226-0

DO - 10.1007/s10951-011-0226-0

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84874109285

SN - 1094-6136

VL - 16

SP - 117

EP - 127

JO - Journal of Scheduling

JF - Journal of Scheduling

IS - 1

ER -