Abstract

Given a set S of strings, a DFA accepting S o#ers a very time-e#cient solution to the pattern matching problem over S. The key is how to implement such a DFA in the trade-o# between time and space, and especially the choice of how to implement the transitions of each state is critical. Bentley and Sedgewick proposed an e#ective tree structure called ternary trees. The idea of ternary trees is to `implant' the process of binary search for transitions into the structure of the trees themselves. This way the process of binary search becomes visible, and the implementation of the trees becomes quite easy. The directed acyclic word graph (DAWG) of a string w is the smallest DFA that accepts all su#xes of w, and requires only linear space. We apply the scheme of ternary trees to DAWGs, introducing a new data structure named ternary DAWGs (TDAWGs). We perform some experiments that show the e#ciency of TDAWGs, compared to DAWGs in which transitions are implemented by tables and linked lists.

Citations