CS 660: SkipLists

CS 660: Combinatorial Algorithms
SkipLists

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San Diego State University -- This page last updated October 10, 1995

Contents of SkipLists Lecture

Skip Lists: BST Las Vegas Style

Skip Lists: BST Las Vegas Style

Level K node - a node with k forward pointers

In above example we have 1/2^k nodes at level k

Need lg(n) levels to act like BST

Let p = be the fraction of the nodes with level j pointers that also have level j + 1 pointers

p = 1/3

Deleting a Node

1. Find the node

2. Remove it
Delete 7

Resultant List

Adding a Node

For a skip list need to select a value for p

1. Select the level of the node

2. Add the node in the proper location

Selecting the level - Theory
Select level k with probability p^k


newLevel = 1;
while random() < p do
: newLevel = newLevel + 1

Selecting the level - Practice
Let N be an upper bound on the number of nodes in the list

Let MaxLevel =

Let CurrentMax be the highest level currently in the list

newLevel = 1;
while random() < p do
: newLevel = newLevel + 1

return min(newLevel, CurrentMax + 1, MaxLevel)

Adding Example, p = 1/3 Add 15

random number generator returns .04 and .672

So level is 2

Resultant List

Timing results

List contains 2¹⁶ elements

Time does not include memory management time

Paper does not include information about access distribution
Time in msec

Algorithm	Search	Insertion	Deletion
Skip List	0.051	0.065	0.059
non-recursive AVL	0.046	0.10	0.085
recursive 2-3 tree	0.054	0.21	0.21
top-down-splay	0.15	0.16	0.18
bottom-up splay	0.49	0.51	0.53

Performance relative to Skip List