University:
University of California, San Diego
Course:
CSE 100/101 | Data Structures and Algorithms
Academic year:

2023
Views:

11

Pages:

2
Author:

anon

Improving the Efficiency of Disjoint Sets with Rooted Trees A collection of sets that are disjoint, or do not share any elements, is a disjoint set data structure. Disjoint sets are frequently used in computer science to maintain track of the connected elements of an undirected graph. The disjoint set data structure can be crudely implemented by encoding each set as a linked list, with the tail of the list denoting the concept of the corresponding set. Merging two sets using this strategy is simple and only requires adding one list to the other. The drawback of this strategy is that as time passes, the lists grow longer and longer, which slows down the "find" process. A more effective method is to visualize each set as a rooted tree, with the concept of each set represented at the tree's root. The "find" action takes less time in this method since each element has a parent that is stored in an array. Creating a Singleton Set Making a singleton set is the first step in putting the rooted tree technique into practice. To achieve this, we set the element's parent to equal to itself, resulting in a tree with just one element, which serves as the tree's root. This operation has a fixed running time. Finding the Root of a Set The "find" operation, which is used to identify the set's root that includes a specific element, is then put into action. To accomplish this, we follow the element's parent pointers until we arrive at a root, which is an element whose parent is also an element. This procedure takes a certain amount of time to complete in relation to the tree's height. Merging Two Sets Implementing the "union" operation, which combines two sets into one, is the last step. To accomplish this, we only switch the parent of one root to that of the other root. This operation has a fixed running time. Improving the Efficiency of the "Find" Operation The "find" operation can be made even more effective by employing strategies like path compression and union by rank. By making the discovered root the parent of the elements on the path from the element to the root, path compression is an optimization that flattens the tree. The optimization known as union by rank always connects the smaller tree to the larger tree's root, which aids in minimizing the height of the trees. In this article, the rooted tree implementation strategy for the disjoint set data structure was discussed. This method is more effective than the conventional linked list method, and it can be made even more effective by using methods like path compression and union by rank. These improvements make it possible to efficiently track the connected parts of an undirected graph using the disjoint set data structure.