The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: What's Past is Prolog
Figure: Two different tries for the given set of rule heads
``In order to speed up unification, we want to preprocess the set of rule heads so that we can quickly
determine which rules match a given goal. We must organize the rules in a trie data structure for fast
unification.''
Tries are extremely useful data structures in working with strings, as discussed in Section . Every leaf
of the trie represents one string. Each node on the path from root to leaf is labeled with exactly one
character of the string, with the ith node of the path corresponding to the ith character of the string.
``I agree. A trie is a natural way to represent your rule heads. Building a trie on a set of strings of
characters is straightforward - just insert the strings one after another starting from the root. So what is
your problem?'' I asked.
``The efficiency of our unification algorithm depends very much on minimizing the number of edges in
the trie. Since we know all the rules in advance, we have the freedom to reorder the character positions in
the rules. Instead of the root node always representing the first argument in the rule, we can choose to
have it represent the third argument. We would like to use this freedom to build a minimum-size trie for
the set of rules.''
He showed me the example in Figure . A trie constructed according to the original string position
order (1, 2, 3) uses a total of 12 edges. However, by permuting the character order to (2, 3, 1), we can
obtain a trie with only 8 edges.
``Why does the speed of unification depend on minimizing the number of edges in the trie?''
``An open goal is one with all distinct variables in its arguments, like p(X,Y,Z). Open goals match
everything. In unifying an open goal against a set of clause heads, each symbol in all the clause heads
will be bound to some variable. By doing a depth-first traversal of this minimum-edge trie, we minimize
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