A trie [11] is one of the best data structures for implementing and searching a dictionary. However, to build the trie structure for larger collections of strings takes up a lot of memory. Since the extended Burrows-Wheeler Transform (XBWT) [8,9] is able to compactly represent a labeled tree, it can naturally be used to succinctly represent a trie. The XBWT also supports navigational operations on the trie, but it does not support failure links. For example, the Aho-Corasick algorithm [1] for simultaneously searching for several patterns in a text achieves its good worst-case time complexity only with the aid of failure links. Manzini [18] showed that a balanced parentheses sequence P can be used to support failure links in constant time with only 2n + o(n) bits of space, where n is the number of internal nodes in the trie. Besides practical algorithms that construct the XBWT, he also provided two different algorithms that construct P. In this paper, we suggest an alternative way for constructing P that outperforms the previous algorithms.
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