Parallel randomized load balancing

It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds (logn=log logn) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the least full of its chosen bins 2]. They show that the fullest bin contains only loglogn=logd + (1) balls with high probability. We explore extensions of this result to parallel and distributed settings. Our results focus on the tradeo between the amount of communication and the nal load. Given r rounds of communication, we provide lower bounds on the maximum load of ( rp logn=loglog n) for a wide class of strategies. Our results extend to the case where the number of rounds is allowed to grow with n. We then demonstrate parallelizations of the sequential strategy presented in Azar et al. that achieve loads within a constant factor of the lower bound for two communication rounds and almost match the s...

• Type: Journal
• Year: 1998
• Where: RSA
• Authors: Micah Adler, Soumen Chakrabarti, Michael Mitzenmacher, Lars Eilstrup Rasmussen
• Keywords: Azar Et Al, Fullest Bin, Lower Bound, RSA 1998