in the trie has at least two children it enforces this rule by compressing chains of single-child nodes into individual edges (see figure let be standard trie we say that an internal node of is redundant if has one child and is not the root for examplethe trie of figure has eight redundant nodes let us also say that chain of > edges( , )( , ( - , )is redundant ifv is redundant for - and are not redundant we can transform into compressed trie by replacing each redundant chain ( , ( - , of > edges into single edge ( )relabeling with the concatenation of the labels of nodes figure compressed trie for the strings bearbellbidbullbuysellstockstop compare this with the standard trie shown in figure thusnodes in compressed trie are labeled with stringswhich are substrings of strings in the collectionrather than with individual characters the advantage of compressed trie over standard trie is that the number of nodes of the compressed trie is proportional to the number of strings and not to their total lengthas shown in the following proposition (compare with proposition proposition compressed trie storing collection of strings from an alphabet of size has the following propertiesevery internal node of has at least two children and most children