The described process continues until there are no unexplored vertices left in the priority queue. Vertex cost reduction is also referred to as a relaxation procedure.Īfter visiting and conditionally updating all the adjoining, non-explored vertices, the vertex being explored will be marked as explored and will not participate in any further algorithm calculations. Otherwise, it will assume the new cost (its cost will decrease) and the vertex in focus will become its ancestor vertex. If the current cost of the adjoining vertex is still lower than the potential new cost, the vertex will not be updated. Its new cost is calculated as the cost of the vertex being explored + the weight of the adjoining edge (the between the vertex being explored and the adjoining vertex). The update condition is determined by comparing each adjoining vertex’s current cost with its new, potentially lower cost. The update operation implies two steps: assignment of the lower cost to the adjoining node and association with the ancestor vertex for later reconstruction of the shortest path. In each following iteration, the vertex with the lowest cost is taken out of the priority queue and its exploration starts by visiting and conditionally updating all adjoining, non-explored vertices. Finally, the starting vertex is marked as explored and does not participate in any further algorithm calculations. After being visited, each adjoining vertex is added to the priority queue. It sets the cost of the starting vertex to 0 and updates the costs of all adjoining, unexplored vertices, according to the weights (distances) associated with the connecting edges. Algorithm Overview: How Does Dijkstra Work?ĭijkstra’s algorithm assumes the cost of all vertices except the starting one as infinite.
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