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Route Planning Dijkstra Algorithm * @param d matrix of distances * @param p matrix of predecessors */ for (int k = 0; k < d.length; k++) { for (int i = 0; i < d.length; i++) { for (int j = 0; j < d.length; j++) { if (d[i][k]==Integer.MAXVALUE||d[k][j]==Integer.MAXVALUE){ continue ; } if (d[i][j] > d[i][k] + d[k][j]) { d[i][j] = d[i][k] + d[k][j]; p[i][j] = p[k][j]; } } } } The algorithm consists of three for loops and it compares all paths in graph between each vertices. It works well but with more density graph the asymptotic complexity rises up and this may causes that the algorithm is too slow to solve the shortest path problem. The algorithm returns shortest path value among all pairs of vertices and there must be constructed the matrix of predecessors to get the output shortest path. 6.5 Dijkstra Algorithm The Dijkstra algorithm was published in 1959 by dutch scientist Edsger W. Dijkstra. This algorithm can find the single-pair shortest path between vertices in graph and it exists in many kind of implementation. The edges can’t be negative length. We can say that this algorithm is basically kind of form of breadth-first search algorithm, in which the order of traversed noded is not determined by number of edges from the root, but as a distance from the root. As a consequence Dijkstra’s algorithm process only those node, for which the shortest path was already discovered. The algorithm stores all nodes in a priority queue ordered by distance of the node from the root – in the first iteration of the algorithm, only root has distance set to 0, distance of all other nodes is equal to infinity. Than in each step Dijkstra’s algorithm picks from the queue a node with the highest priority (least distance from the root) a processes it and reevaluates distances of all unprocessed descendants of the node[23; Kola ́ˇr, 2004]. The algorithm has without modification an asymptotic complexity as O(|V |2), where V is 26PDF Image | Driving Range Estimation and Trajectory Planning
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