Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007
Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1+o(1)) ln n/ln ln n balls in it. Suppose instead that for each ball we choose two boxes at random and place the ball into the one which is less full at the time of placement. We show that with high probability, the fullest box contains only ln ln n/ln 2+O(1) balls - exponentially less than before. Furthermore, we show that a similar gap exists in the infinite process, where at each step one ball, chosen uniformly at random, is deleted, and one ball is added in the manner above. We discuss consequences of this and related theorems for dynamic resource allocation, hashing, and on-line load balancing.
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007
Lixi Zhou, Jiaqing Chen, et al.
VLDB
S.M. Sadjadi, S. Chen, et al.
TAPIA 2009
Michael C. McCord, Violetta Cavalli-Sforza
ACL 2007