What is the significance of the edge relaxation heap in the Dijkstra Algorithm?

Dijkstra Algorithm Questions



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What is the significance of the edge relaxation heap in the Dijkstra Algorithm?

The edge relaxation heap is significant in the Dijkstra Algorithm as it helps to efficiently select the next vertex with the minimum distance from the source vertex. It allows for the constant time extraction of the vertex with the minimum distance, ensuring that the algorithm runs in a time complexity of O((V + E) log V), where V is the number of vertices and E is the number of edges in the graph. This heap data structure helps in maintaining the priority queue of vertices based on their distances, enabling the algorithm to find the shortest path efficiently.