[3] In the fully persistent model, both updates and queries are allowed on any version of the data structure.
One of the technique is by using randomized version of Van Emde Boas Tree which is created using dynamic perfect hashing.
In order to navigate through the structure, each original field value in a node has a version stamp of zero.
In a Balanced Binary Search Tree without parent pointers the worst case modification time complexity is O(log n + update cost).
However, in a linked list the worst case modification time complexity is O(n + update cost).
Driscoll, Sarnak, Sleator, Tarjan came up[1] with a way to combine the techniques of fat nodes and path copying, achieving O(1) access slowdown and O(1) modification space and time complexity.
Putting it all together, the change in ϕ is Δϕ =1− k. Thus, the algorithm takes O(k +Δϕ)= O(1) space and O(k +Δϕ +1) = O(1) time Path copying is one of the simple methods to achieve persistency in a certain data structure such as binary search trees.
In order to achieve that, we consider a directed graph G. We assume that each vertex v in G has a constant number c of outgoing edges that are represented by pointers.
Each row contains in addition to the pointers for the outgoing edges, a label which represents the data at the vertex and a time t at which the operation was performed.
Therefore, the amount of work required to complete a sequence of operations is bounded by the number of tables created multiplied by
Many common reference-based data structures, such as red–black trees,[7] stacks,[8] and treaps,[9] can easily be adapted to create a persistent version.
Some others need slightly more effort, for example: queues, dequeues, and extensions including min-deques (which have an additional O(1) operation min returning the minimal element) and random access deques (which have an additional operation of random access with sub-linear, most often logarithmic, complexity).
One primary advantage to using purely persistent data structures is that they often behave better in multi-threaded environments.
[10] Some ML-derived languages, like Haskell, are purely functional because once a node in the list has been allocated, it cannot be modified, only copied, referenced or destroyed by the garbage collector when nothing refers to it.
A function which inserts data into the binary tree and maintains the invariant is:After executing The following configuration is produced:
GitHub repo containing implementations of persistent BSTs using Fat Nodes, Copy-on-Write, and Path Copying Techniques.
To use the persistent BST implementations, simply clone the repository and follow the instructions provided in the README file.
This paper presented a mutable Hash table where "Insert, search and delete times are small and constant, independent of key set size, operations are O(1).
[12] This data structure was then modified by Rich Hickey to be fully persistent for use in the Clojure programming language.
[13] Conceptually, hash array mapped tries work similar to any generic tree in that they store nodes hierarchically and retrieve them by following a path down to a particular element.
This means that in practice while insertions, deletions, and lookups into a persistent hash array mapped trie have a computational complexity of O(log n), for most applications they are effectively constant time, as it would require an extremely large number of entries to make any operation take more than a dozen steps.
These data structures implement the mandatory read-only parts of the Java collections framework.
[21] The designers of the Clojure language advocate the use of persistent data structures over mutable data structures because they have value semantics which gives the benefit of making them freely shareable between threads with cheap aliases, easy to fabricate, and language independent.
[23] The Elm programming language is purely functional like Haskell, which makes all of its data structures persistent by necessity.
Despite this, the core JDK package java.util.concurrent includes CopyOnWriteArrayList and CopyOnWriteArraySet which are persistent structures, implemented using copy-on-write techniques.
The Redux library is inspired by the state management pattern used in the Elm programming language, meaning that it mandates that users treat all data as persistent.
[29] As a result, the Redux project recommends that in certain cases users make use of libraries for enforced and efficient persistent data structures.
This reportedly allows for greater performance than when comparing or making copies of regular JavaScript objects.
Some Prolog systems nevertheless do provide destructive operations like setarg/3, which might come in different flavors, with/without copying and with/without backtracking of the state change.
[39] In some platforms where persistent data structures are used it is an option to not use garbage collection which, while doing so can lead to memory leaks, can in some cases have a positive impact on the overall performance of an application.