Skip Lists: A Probabilistic Alternative to Balanced Trees

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at:, or follow me on Twitter.


Skip lists are a data structure that can be used in place of balanced trees.
Skip lists use probabilistic balancing rather than strictly enforced balancing
and as a result the algorithms for insertion and deletion in skip lists are
much simpler and significantly faster than equivalent algorithms for
balanced trees

A node that has k forward pointers is called a level k node.
If every (2i)th node has a pointer 2i nodes ahead, then levels
of nodes are distributed in a simple pattern: 50% are level 1,
25% are level 2, 12.5% are level 3 and so on. What would
happen if the levels of nodes were chosen randomly, but in the
same proportions (e.g., as in Figure 1e)? A node’s i’th forward
pointer, instead of pointing 2i–1 nodes ahead, points to the
next node of level i or higher. Insertions or deletions would
require only local modifications; the level of a node, chosen
randomly when the node is inserted, need never change. Some
arrangements of levels would give poor execution times, but
we will see that such arrangements are rare. Because these
data structures are linked lists with extra pointers that skip
over intermediate nodes, I named them skip lists.

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