 
Summary: The Expansion and Mixing Time of Skip Graphs
with Applications
James Aspnes
Udi Wieder §
June 11, 2008
Abstract
We prove that with high probability a skip graph contains a 4regular expander as a subgraph
and estimate the quality of the expansion via simulations. As a consequence, skip graphs contain
a large connected component even after an adversarial deletion of nodes. We show how the
expansion property can be used to sample a node in the skip graph in a highly efficient manner.
We also show that the expansion property can be used to load balance the skip graph quickly.
Finally, it is shown that the skip graph could serve as an unstructured P2P system, making it
a good candidate for a hybrid P2P system.
1 Introduction
Skip graphs [3] and SkipNets [7] are randomized distributed data structures designed for use in peer
topeer (P2P) storage systems. Like Distributed Hash Tables (DHTs), skip graphs scale gracefully,
and offer excellent query complexity [14]. Skip graphs have an advantage over DHTs in that they
directly support range queries, while DHTs provide exact search only. Much of the usefulness of
skip graphs depends on their properties as random graphs. It was previously shown [3] that (with
high probability) skip graphs have expansion ratio (1/ log n): every subset of m n/2 nodes of a
