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 for iterative deepening
From The Free On-line Dictionary of Computing (30 December 2018) :

  iterative deepening
      A graph search algorithm that will find the
     shortest path with some given property, even when the graph
     contains cycles.  When searching for a path through a graph,
     starting at a given initial node, where the path (or its end
     node) has some desired property, a depth-first search may
     never find a solution if it enters a cycle in the graph.
     Rather than avoiding cycles (i.e. never extend a path with a
     node it already contains), iterative deepening explores all
     paths up to length (or "depth") N, starting from N=0 and
     increasing N until a solution is found.

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