Complexity of trie index construction

Trie structures are a convenient way of indexing files in which keys are specified by values of attributes. Records correspond to leaves in the trie. Retrieval proceeds by following a path from the root to a leaf, the choice of edges being determined by attribute values. The size of a trie for a file depends on the order in which attributes are tested. We show that determining minimal size tries is an NP-complete problem for several variants of tries. For tries in which leaf chains are deleted we show that determining the trie for which average access time is minimal is also an NP-complete problem. Our results hold even for files in which attribute values are chosen from a binary or ternary alphabet.