Balanced Allocation and Dictionaries with Tightly Packed Constant Size Bins

We study a particular aspect of the balanced allocation paradigm (also known as the “two-choices paradigm”): constant sized bins, packed as tightly as possible. Let d ≥ 1 be fixed, and assume there are m bins of capacity d each. To each of n ≤ dm balls two possible bins are assigned at random. How close can dm/n = 1 + ε be to 1 so that with high probability each ball can be put into one of the two bins assigned to it without any bin overflowing? We show that ε > (2/e)d−1 is sufficient. If a new ball arrives with two new randomly assigned bins, we wish to rearrange some of the balls already present in order to accommodate the new

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Martin Dietzfelbinger, Christoph Weidling
• Keywords: Balanced Allocation Paradigm, Constant Sized Bins, ICALP 2005, Possible Bins, Theoretical Computer Science