File:Dijkstra-negative-edge-weights-error.svg

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Deutsch: Beispiel, warum negative Kantengewichte nicht zulässig sind: Startend in Knoten eins, wird Dijkstra im ersten Schritt d(zwei)=1 und d(vier)=4 setzen, d(zwei) ist am kleinsten, folglich wird im nächsten Schritt d(drei)=2 gesetzt. d(drei) ist kleiner als d(vier), hat aber keine weiteren Nachbarn. Folglich wird Knoten vier als letztes betrachtet und damit niemals die negative Kante (4,3), da Dijkstra zuvor abbricht.
English: Dijkstra's algorithm doesn't work with negative edge weights. For instance, consider the graph: Starting in vertex 1, Dijkstra's algorithm will choose the edge (1,2) setting dist(vertex 2)=1 and edge (1,4) setting dist(vertex 4)=4. dist(vertex 2) is smallest distance, so Dijkstra will choose edge (2,3) setting dist(vertex 3)=2. Smallest distance is dist(vertex 3). Because vertex 4 is the last one visited, it never finds the shortest path from 1 to 3, via 4, with total length 1.
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Source Redrawn in SVG, original PNG Dijkstra negative edge weights error.png by Chin tin tin
Author Stkl
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