A Faster Scrabble Move Generation Algorithm

Appel and Jacobson1 presented a fast algorithm for generating every possible move in a given position in the game of Scrabble using a DAWG, a finite automaton derived from the trie of a large lexicon. This paper presents a faster algorithm that uses a GADDAG, a finite automaton that avoids the non-deterministic prefix generation of the DAWG algorithm by encoding a bidirectional path starting from each letter of each word in the lexicon. For a typical lexicon, the GADDAG is nearly five times larger than the DAWG, but generates moves more than twice as fast. This time/space trade-off is justified not only by the decreasing cost of computer memory, but also by the extensive use of move-generation in the analysis of board positions used by Gordon in the probabilistic search for the most appropriate play in a given position within realistic time constraints.