Source : Free On-Line Dictionary of Computing

iterative deepening
     
        A graph search algorithm.  When searching for a path through a
        graph from a given initial node to a solution node with some
        desired property, a {depth-first search} may never find a
        solution if it enters a cycle in the graph.  We can either add
        an explicit check for cycles so that we never extend a path
        with a node it already contains or we can use iterative
        deepening where we explore all paths up to length (or "depth")
        N, starting from N=0 and increasing N until a solution is
        found.
     
        (1995-02-14)