Balls-and-bins games have been a successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball-recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a given probability distribution p. Then, at each time step, pick a non-empty bin and recycle its balls: take the balls from the selected bin and re-throw them according to p. This balls-and-bins game closely models memory-access heuristics in databases. The goal is to have a bin-picking method that maximizes the recycling rate, defined to be the expected number of balls recycled per step in the stationary distribution. We study two natural strategies for ball recycling: Fullest Bin, which greedily picks the bin with the maximum number of balls, and Random Ball, which picks a ball at random and recycles its bin. We show that for general p, Random Ball is Θ(1)-optimal, whereas Fullest Bin can be pessimal. However, when p = u, the uniform distribution, Fullest Bin is optimal to within an additive constant.
|Number of pages||20|
|State||Published - 1 Jan 2019|
|Event||30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States|
Duration: 6 Jan 2019 → 9 Jan 2019
|Conference||30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019|
|Period||6/01/19 → 9/01/19|