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. (2004-01-26)