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Using min heap priority queue in Prim's algorithm to find the minimum spanning tree of a connected and undirected graph, one can achieve a good running time. This min heap priority queue uses the min heap data structure which supports operations such as insert , minimum , extract-min , decrease-key . [ 23 ]
For sparse graphs, that is, graphs with far fewer than | | edges, Dijkstra's algorithm can be implemented more efficiently by storing the graph in the form of adjacency lists and using a self-balancing binary search tree, binary heap, pairing heap, Fibonacci heap or a priority heap as a priority queue to implement extracting minimum efficiently.
Queue (example Priority queue) Double-ended queue; Graph (example Tree, Heap) ... Many graph-based data structures are used in computer science and related fields:
Prim's algorithm has many applications, such as in the generation of this maze, which applies Prim's algorithm to a randomly weighted grid graph. The time complexity of Prim's algorithm depends on the data structures used for the graph and for ordering the edges by weight, which can be done using a priority queue. The following table shows the ...
A bucket queue is a data structure that implements the priority queue abstract data type: it maintains a dynamic collection of elements with numerical priorities and allows quick access to the element with minimum (or maximum) priority. In the bucket queue, the priorities must be integers, and it is particularly suited to applications in which ...
A priority queue is an abstract data-type similar to a regular queue or stack. Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority. Priority queues support the following operations: insert: add an element to the queue with an associated priority.
Best-first search: traverses a graph in the order of likely importance using a priority queue; Bidirectional search: find the shortest path from an initial vertex to a goal vertex in a directed graph; Breadth-first search: traverses a graph level by level
This priority queue is known as the open set, fringe or frontier. At each step of the algorithm, the node with the lowest f ( x ) value is removed from the queue, the f and g values of its neighbors are updated accordingly, and these neighbors are added to the queue.