TY - GEN
T1 - Randomized algorithms for online vector load balancing
AU - Azar, Yossi
AU - Cohen, Ilan Reuven
AU - Panigrahi, Debmalya
N1 - Publisher Copyright:
© Copyright 2018 by SIAM.
PY - 2018
Y1 - 2018
N2 - We study randomized algorithms for the online vector bin packing and vector scheduling problems. For vector bin packing, we achieve a competitive ratio of ~O(d1=B), where d is the number of dimensions and B the size of a bin. This improves the previous bound of Õ(d1B)) by a polynomial factor, and is tight up to logarithmic factors. For vector scheduling, we show a lower bound of ( log d log log d ) on the competitive ratio of randomized algorithms, which is the first result for randomized algorithms and is asymptotically tight. Finally, we analyze the widely used "power of two choices' algorithm for vector scheduling, and show that its competitive ratio is O(log log n+ log d log log d ), which is optimal up to the additive O(log log n) term that also appears in the scalar version of this algorithm.
AB - We study randomized algorithms for the online vector bin packing and vector scheduling problems. For vector bin packing, we achieve a competitive ratio of ~O(d1=B), where d is the number of dimensions and B the size of a bin. This improves the previous bound of Õ(d1B)) by a polynomial factor, and is tight up to logarithmic factors. For vector scheduling, we show a lower bound of ( log d log log d ) on the competitive ratio of randomized algorithms, which is the first result for randomized algorithms and is asymptotically tight. Finally, we analyze the widely used "power of two choices' algorithm for vector scheduling, and show that its competitive ratio is O(log log n+ log d log log d ), which is optimal up to the additive O(log log n) term that also appears in the scalar version of this algorithm.
UR - http://www.scopus.com/inward/record.url?scp=85045579097&partnerID=8YFLogxK
U2 - 10.1137/1.9781611975031.63
DO - 10.1137/1.9781611975031.63
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AN - SCOPUS:85045579097
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 990
EP - 991
BT - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
A2 - Czumaj, Artur
PB - Association for Computing Machinery
T2 - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Y2 - 7 January 2018 through 10 January 2018
ER -