4.2. The analysis 91
Therefore, the convexity of the function logx implies that B1 g 0.
(See Section 4.4.) To bound B2, we argue as follows:
- 2 - 2
B2 = z'log
Recall that 2' = [3/2]. Ifj : 27L, then wj 2 2j3 : 2 - 87:3 2 811),. If
64 3. Range Trees and the PostOice Problem
at this moment, we have |Svl = 1. The size of C is bounded by 0(log
Therefore, this nal step takes O(log n) time.
We have shown that the algorithm nds a rightLooneighbor of p
in O(logn)2) time. In the same amoun
1.5. Tail estimates: Cherno bounds 19
1.5 Tail estimates: Cherno' bounds
In the previous section, we proved bounds for the expected size, search
time and update time of a skip list. In this section, we consider so-
called tail estimates. That is, we estim