Before revision:  We show that  the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's high-order worst-case entropyH. We finally present the first trie index able to locate in pre-order nodes reached by a path labeled with a given pattern. Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n)  + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
After revision:  We show that the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's repetitiveness and lower-bounds a natural notion of trie entropy. Our main contribution is a much deeper insight into the combinatorial structure of this object. In detail, we show that a data structure of O(r log n) \leq 2n + o(n) + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .