It is the final inner loop that is problematic. Instead, your graph should comprise movies and actors as vertices (edge = actor was in a given movie), and to g

It is the final inner loop that is problematic. Instead, your graph should comprise movies and actors as vertices (edge = actor was in a given movie), and to get the Bacon number you just halve the distance in this graph. So you code would look like for bucket in hashtable: add node for bucket for actor in bucket: if actor not in graph, add a node for actor add an edge between actor and bucket add an edge between bucket and actor If each movie contains exactly K actors, and there are N movies, then your graph has O(NK^2) edges while mine has O(NK) edges.