Optimal Ball Recycling
Abstract
Ballsandbins games have been a wildly 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 nonempty bin and recycle its balls: take the balls from the selected bin and rethrow them according to p. This ballsandbins game closely models memoryaccess heuristics in databases. The goal is to have a binpicking 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 constantoptimal, whereas Fullest Bin can be pessimal. However, when p = u, the uniform distribution, Fullest Bin is optimal to within an additive constant.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.01804
 Bibcode:
 2018arXiv180701804B
 Keywords:

 Computer Science  Data Structures and Algorithms