4.4 Shortest Paths
PERHAPS THE MOST INTUITIVE graph-processing problem is one that you encounter regularly, when using a map application or a navigation system to get directions from one place to another. A graph model is immediate: vertices correspond to intersections and edges correspond to roads, with weights on the edges that model the cost, perhaps distance or travel time. The possibility of one-way roads means that we will need to consider edge-weighted digraphs. In this model, the problem is easy to formulate:
Find a lowest-cost way to get from one vertex to another.
Beyond direct applications of this sort, the shortest-paths model is appropriate for a range of other problems, some of which do not seem to be at all related to graph processing. ...
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