Concurrent Binary Search Tree Implementation in Python

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Data Structures

Introduction

This article presents a concurrent binary search tree implementation in Python, designed to be concise and easy to understand. We will discuss the class definition, followed by the implementation of concurrent search, insert, delete, and update operations. Finally, we will provide an example of executing these operations concurrently. Binary search trees (BSTs) are a widely used data structure due to their efficient search, insertion, and deletion capabilities. A BST is a tree-like data structure where each node has at most two children, and for all nodes, the left child node is less than the parent node, and the right child node is greater than the parent node.

The time complexity for search, insert, and delete operations is generally O(h), where h is the height of the tree. In a balanced tree, the height is O(log n), where n is the number of nodes. In concurrent programming, multiple threads execute simultaneously, and concurrent access to shared data structures, such as a binary search tree, can lead to unpredictable results if not handled correctly. A concurrent binary search tree ensures that these operations are thread-safe, allowing multiple threads to access and modify the tree without causing data corruption or race conditions.

Concurrent Binary Search Tree Implementation in Python

Concurrent Binary Search Tree Python Class Definition

To implement a concurrent binary search tree in Python, we first define a class ConcurrentBinarySearchTree with a generic type parameter T. This class requires that the items stored in the tree are comparable, which is a fundamental requirement for the operations of a binary search tree. The class exposes four main methods: search, insert, delete, and update.

from threading import Lock

class Node:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

class ConcurrentBinarySearchTree:
    def __init__(self):
        self.root = None
        self.lock = Lock()
        # Scroll down for methods implementation
        # ...
  • The search operation checks if an item exists within the tree and returns True if found, otherwise False. The time complexity of the search operation is O(h), where h is the height of the tree.
  • The insert operation adds a new item to the tree while maintaining the binary search tree property. The time complexity of the insert operation is O(h), where h is the height of the tree.
  • The delete operation removes an item from the tree and rearranges the tree to maintain its properties. The time complexity of the delete operation is O(h), where h is the height of the tree.
  • The update operation updates an existing item in the tree with a new item while maintaining the binary search tree property. The time complexity of the update operation is O(h), where h is the height of the tree.

The next sections of this article will explain the concurrent implementations of these operations, ensuring thread-safety and efficient performance while maintaining the binary search tree properties.

Concurrent Search Operation Implementation in Binary Search Tree

The concurrent search operation allows multiple threads to search for items within the binary search tree simultaneously without causing data corruption. The search operation does not modify the tree structure, so thread-safety is achieved without the need for locks or other synchronization mechanisms.

In the search operation, we traverse the tree, starting from the root node, comparing the target item with each node’s value. If the target item is less than the current node’s value, we move to the left child; otherwise, we move to the right child. Whenever we reach a null reference, the item is not in the tree, and we return False. If we find a node with the same value as the target item, we return True. The time complexity of the search operation is O(h), where h is the height of the tree. In the worst case, we need to traverse the entire height of the tree.

def search(self, item):
    # Traverses the tree, comparing each node's value with the target item.
    # If found, it returns True. Otherwise, it returns False.
    current = self.root

    while current is not None:
        comparison = self._compare(item, current.value)

        if comparison == 0:
            return True
        current = current.left if comparison < 0 else current.right

    return False

Concurrent Insert Operation Implementation in Binary Search Tree

The concurrent insert operation adds a new item to the tree while maintaining the binary search tree property. To ensure thread-safety, we use a lock when modifying the tree structure. This prevents multiple threads from inserting nodes simultaneously, which could lead to data corruption.

In the insert operation, we traverse the tree to find the position for the new item. We compare the new item with each node’s value during the traversal. If the new item is less than the current node’s value, we move to the left child; otherwise, we move to the right child. If we find a node with the same value as the new item, the insertion is a duplicate, and we return False. Once we reach a null reference, we have found the position for the new item. We then lock the tree to prevent other threads from modifying it while we insert the new node. The time complexity of the insert operation is O(h), where h is the height of the tree.

def insert(self, item):
    # Inserts a new node by finding its position in the tree.
    # Uses a lock to ensure thread-safety during the process.
    new_node = Node(item)
    parent = None
    current = self.root

    while current is not None:
        parent = current
        comparison = self._compare(item, current.value)

        if comparison == 0:
            return False
        current = current.left if comparison < 0 else current.right

    with self.lock:
        if parent is None:
            self.root = new_node
        elif self._compare(item, parent.value) < 0:
            parent.left = new_node
        else:
            parent.right = new_node

    return True

Concurrent Delete Operation Implementation

The concurrent delete operation removes an item from the tree and rearranges the tree to maintain the binary search tree property. To ensure thread-safety, we use a lock when modifying the tree structure. The delete operation involves three main scenarios:

  1. The node to delete has no children: In this case, we simply remove the node from the tree and update its parent’s reference.
  2. The node to delete has one child: We remove the node from the tree and update its parent’s reference to point to the node’s single child.
  3. The node to delete has two children: We find the node with the minimum value in the right subtree (the inorder successor), replace the node to delete with the inorder successor’s value, and then delete the inorder successor.

The time complexity of the delete operation is O(h), where h is the height of the tree.

def delete(self, item):
    # Deletes a node with the given item from the tree.
    # Uses a lock to ensure thread-safety during the process.
    parent, node = self._find_node_and_parent(item)
    if node is None:
        return False

    with self.lock:
        self._delete_node(node, parent)

    return True

def _delete_node(self, node, parent):
    if node.left is None and node.right is None:
        self._replace_node_in_parent(parent, node, None)
    elif node.left is not None and node.right is not None:
min_right = self._find_min_node(node.right)
node.value = min_right.value
self._delete_node(min_right, node)
else:
child = node.left if node.left is not None else node.right
self._replace_node_in_parent(parent, node, child)

def _replace_node_in_parent(self, parent, node, new_node):
if parent is None:
self.root = new_node
elif parent.left == node:
parent.left = new_node
else:
parent.right = new_node

def _find_min_node(self, node):
while node.left is not None:
node = node.left
return node

Concurrent Update Operation Implementation

The concurrent update operation updates an existing item in the tree with a new item while maintaining the binary search tree property. To ensure thread-safety, we use a lock when modifying the tree structure. In the update operation, we first delete the old item from the tree, and then insert the new item. By using a lock, we ensure that no other thread can modify the tree between the delete and insert operations. The time complexity of the update operation is O(h), where h is the height of the tree. Since the update operation involves a delete followed by an insert, the complexity remains the same as individual delete and insert operations.

def update(self, old_item, new_item):
    # Updates a node by deleting the old item and inserting the new one.
    # Uses a lock to ensure thread-safety.
    with self.lock:
        if self.delete(old_item):
            return self.insert(new_item)

    return False

Testing the Concurrent Binary Search Tree

import threading

def main():
    tree = ConcurrentBST()
    element_count = 50000

    # Concurrent insertions
    t1 = threading.Thread(target=insert_elements, args=(tree, 1, element_count // 2))
    t2 = threading.Thread(target=insert_elements, args=(tree, element_count // 2 + 1, element_count))

    # Concurrent deletions
    t3 = threading.Thread(target=delete_elements, args=(tree, 1, element_count // 4))
    t4 = threading.Thread(target=delete_elements, args=(tree, element_count // 4 + 1, element_count // 2))

    # Concurrent updates
    t5 = threading.Thread(target=update_elements, args=(tree, 1, element_count // 4, element_count))
    t6 = threading.Thread(target=update_elements, args=(tree, element_count // 4 + 1, element_count // 2, element_count))

    t1.start()
    t2.start()
    t3.start()
    t4.start()
    t5.start()
    t6.start()

    t1.join()
    t2.join()
    t3.join()
    t4.join()
    t5.join()
    t6.join()

    print("Processing completed.")

def insert_elements(tree, start, end):
    for i in range(start, end + 1):
        tree.insert(i)

def delete_elements(tree, start, end):
    for i in range(start, end + 1):
        tree.delete(i)

def update_elements(tree, start, end, offset):
    for i in range(start, end + 1):
        tree.update(i, i + offset)

if __name__ == "__main__":
    main()

Conclusion

This article presented a concurrent binary search tree implementation in Python, designed to be clear and easy to understand. We discussed the class definition and provided a thread-safe implementation of concurrent search, insert, delete, and update operations while maintaining the binary search tree properties. By using a combination of locks and careful consideration of the areas that require synchronization, we achieved an efficient and safe manipulation of the data structure in a multi-threaded environment. The concurrent binary search tree offers time complexities of O(h) for each operation, where h is the height of the tree, making it a valuable data structure for use in concurrent programming scenarios.

With the provided implementation, developers can harness the power of concurrency to optimize the performance of their applications, especially when dealing with large data sets and multiple threads accessing the same data structure. The concurrent binary search tree is an excellent choice for scenarios where the data needs to be accessed, modified, or deleted by multiple threads without causing data corruption or race conditions.

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