Paths in graphs


Depth-first search readily identifies all the vertices of a graph that can be reached from a
designated starting point. It also finds explicit paths to these vertices, summarized in its
search tree (Figure 4.1). However, these paths might not be the most economical ones possi-ble. In the figure, vertex C is reachable from S by traversing just one edge, while the DFS tree shows a path of length 3. This chapter is about algorithms for finding shortest paths in graphs.

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