Biased Skip Lists for Highly Skewed Access Patterns

Abstract

Dynamic tables that support search, insert and delete operations are fundamental and well studied in computer science. There are many well known data structures that solve this problem, including balanced binary trees, skip lists and tries among others. Many of the existing data structures work efficiently when the access patterns are uniform, but in many circumstance access patterns are biased. Various data structures have been proposed that exploit bias in access patterns to improve efficiency for the operations they support.

In this paper we introduce a new data structure, the biased skip list (BSL), which is designed to work with biased access distributions. Specifically, given key k, let its rank r(k) be the number of distinct keys accessed since the last access to k. BSL enables one to search for k in O(logr(k)) expected time. Insertions and deletions take O(logr _max (k)) expected time where r _max (k) denotes the maximum rank of k during its lifespan.

Our work is motivated by recent studies on packet filtering and classification where keys have been found to have geometric (or more skewed) access probabilities as a function of how recently they have been accessed. We demonstrate the practicality of BSL with experiments on real and synthetic data with various degrees of bias.