Skewed Binary Search Trees

Gerth Stølting Brodal and Gabriel Moruz

In Proc. 14th Annual European Symposium on Algorithms, volume 4168 of Lecture Notes in Computer Science, pages 708-719. Springer Verlag, Berlin, 2006.

Abstract

It is well-known that to minimize the number of comparisons a binary search tree should be perfectly balanced. Previous work has shown that a dominating factor over the running time for a search is the number of cache faults performed, and that an appropriate memory layout of a binary search tree can reduce the number of cache faults by several hundred percent. Motivated by the fact that during a search branching to the left or right at a node does not necessarily have the same cost, e.g. because of branch prediction schemes, we in this paper study the class of skewed binary search trees. For all nodes in a skewed binary search tree the ratio between the size of the left subtree and the size of the tree is a fixed constant (a ratio of 1/2 gives perfect balanced trees). In this paper we present an experimental study of various memory layouts of static skewed binary search trees, where each element in the tree is accessed with a uniform probability. Our results show that for many of the memory layouts we consider skewed binary search trees can perform better than perfect balanced search trees. The improvements in the running time are on the order of 15%.

Copyright notice

© Springer-Verlag Berlin Heidelberg 2006. All rights reserved.

Online version

esa06skew.pdf (250 Kb)

DOI

10.1007/11841036_63

Slides

esa06skew.pdf (229 Kb)

BIBTEX entry

@incollection{esa06skew,
  author = "Gerth St{\o}lting Brodal and Gabriel Moruz",
  booktitle = "Proc. 14th Annual European Symposium on Algorithms",
  doi = "10.1007/11841036_63",
  isbn = "978-3-540-38875-3",
  pages = "708-719",
  publisher = "Springer {V}erlag, Berlin",
  series = "Lecture Notes in Computer Science",
  title = "Skewed Binary Search Trees",
  volume = "4168",
  year = "2006"
}