Randomization of Search Trees by Subtree Size
نویسندگان
چکیده
In this paper we present probabilistic algorithms over random binary search trees such that: a) the insertion of a set of keys in any xed order into an initially empty tree produces always a random tree; b) the deletion of any key of a random tree results in a random tree; c) the random choices made by the algorithms are based upon the sizes of the subtrees of the random tree, an information that can be used for rank searches, for instance; and d) the cost, measured as the number of visited nodes, of any elemental operation is the same as the cost of the standard deterministic version, with less than two expected rotation-like operations per update.
منابع مشابه
The Subtree Size Profile of Bucket Recursive Trees
Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial...
متن کاملSubtree Sizes in Recursive Trees and Binary Search Trees: Berry-Esseen Bounds and Poisson Approximations
We study the number of subtrees on the fringe of random recursive trees and random binary search trees whose limit law is known to be either normal or Poisson or degenerate depending on the size of the subtree. We introduce a new approach to this problem which helps us to further clarify this phenomenon. More precisely, we derive optimal Berry-Esseen bounds and local limit theorems for the norm...
متن کاملThe Coast of Searching in General Trees versus Complete Binary Trees
We consider the problem of searching in natural families of trees. A search in a tree T is a sequence of queries used to locate a pre-designated node called the \buggy" node. A query is made to any subtree in T. If the queried subtree contains the buggy node, then we restrict the search to that subtree, otherwise the search is restricted to the complement of that subtree in T. Two problems are ...
متن کاملKaikoura Information Processing Letters tree theorems : Computing the maximum agreement subtree
The Maximum Agreement Subtree Problem was posed by Finden and Gordon in 1985, and is as follows: given a set S={s,, sz,..., s,,} and two trees P and Q leaf-labelled by the elements of S, find a maximum cardinality subset S, of S such that PI S, = Q IS,. This problem arises in evolutionary tree construction, where different methods or data yield (possibly) different trees for the same species on...
متن کاملFibonacci BSTs: A new balancing method for binary search trees
This paper presents a newmethod to balance binary search trees, which has the following properties. (i) The only information stored for the balance is the size of every subtree. (ii) Inserting or deleting an element can be done in themost traditional way: first, the element is recursively inserted (deleted) in (from) the appropriate subtree; afterwards, a single or double rotation takes place i...
متن کامل